NSTL国家科技图书文献中心

1. Estimates of Approximation Numbers, Nuclearity of the Resolvent of a Third-Order Singular Differential Operator, and the Completeness of Its Root Vectors NSTL国家科技图书文献中心

Muratbekov, Mussakan | Muratbekov, Madi ... - 《Mathematical Methods in the Applied Sciences》 - 2025,48(8) - 8903～8910 - 共8页

摘要： singular differential operator in the space L2(& Ropf | third-order differential* operator and demonstrate the* | solutions to the equation associated with the operator. We | and obtain two-sided bounds for the singular* numbers* | the resolvent of the operator* under consideration*

关键词： approximation numbers | completeness of root vectors | nuclearity | resolvent | separability | singular operator | third-order differential operator | third‐order differential operator

2. Cubic spline quasi-interpolation operator to numerically solve integro-differential equations with weakly singular kernels NSTL国家科技图书文献中心

C. Allouch | D. Barrera ... - 《Mathematics and computers in simulation》 - 2025,230(Apr.) - 413～422 - 共10页

摘要：-differential* equation with weakly singular kernel. Also, some* | -interpolant operator* to numerically address a class of* | linear integro-differential* equations with weakly* | singular kernel. As stated in Pedas and Tamme (2006), the | quasi-interpolant operator* in this particular space*

关键词： Quasi-interpolants operators | Fredholm integro-differential equations | Weakly singular kernel | Graded grids

3. QUASI-PERIODIC SOLUTIONS FOR THE DERIVATIVE NONLINEAR SCHROEDINGER EQUATIONS WITH UNBOUNDED LEGENDRE POTENTIALS NSTL国家科技图书文献中心

XUEMEI LI | GUANGHUA SHI - 《Discrete and continuous dynamical systems》 - 2025,45(2) - 607～664 - 共58页

摘要：In this paper, the derivative nonlinear | Schroedinger equations with Legendre potential i | |~2 _ = 0 subject to certain boundary | conditions was considered, where the potential function | ( ) = 1/2 1/4tan~2 , ( /2 , /2), has

关键词： Completely resonant | quasi-periodic solutions | KAM for PDE | singular differential operator | small divisors

4. Solvability Theory for Singular Integro-Differential Equations in the Class of Generalized Functions NSTL国家科技图书文献中心

Gabbasov, N. S. - 《Computational mathematics and mathematical physics》 - 2025,65(1) - 89～101 - 共13页

摘要： singular differential operator in the principal part is | A linear integro-differential* equation with a* | studied. For its approximate solution in the space of | generalized functions, a special generalized version of the | collocation method is proposed and substantiated.

关键词： integro-differential equation | approximate solution | direct method | theoretical justification

5. A nonlocal Kirchhoff diffusion problem with singular potential and logarithmic nonlinearity NSTL国家科技图书文献中心

Tan, Zhong | Yang, Yi - 《Mathematical Methods in the Applied Sciences》 - 2025,48(2) - 2561～2583 - 共23页

摘要： by a nonlocal integro- differential* operator L-K:u* | In this paper, we investigate the following | fractional Kirchhoff-type pseudo parabolic equation driven | (s) + M([u](s)(2))L | (K)u + L (K)u(t) = vertical bar u vertical bar(p-2

关键词： blow-up | fractional parabolic problem of Kirchhoff type | logarithmic nonlinearity | nonlocal integro-differential operator | singular potential | blow‐up | nonlocal integro‐differential operator

6. GLOBAL EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NONLINEAR SINGULAR EIGENVALUE PROBLEMS NSTL国家科技图书文献中心

Nikolaos S. Papageor... | Jian Zhang ... - 《Discrete and continuous dynamical systems,Series S》 - 2025,18(6) - 1440～1456 - 共17页 - 被引量：16

摘要： operator. The singular term is not decoupled from the | We consider a singular* eigenvalue problem* | driven by a nonlinear nonhomogeneous differential | rest of the reaction, as is the case in most singular | elliptic problems. Using variational tools together with

关键词： Nonlinear nonhomogeneous differential operator | nonlinear regularity theory | truncation | positive solutions | Hardy's inequality

7. ON THE ROBUST STABILITY OF VOLTERRA DIFFERENTIAL-ALGEBRAIC SYSTEMS NSTL国家科技图书文献中心

Ha, Nguyen thu | Cuong, Tran manh - 《Communications on pure and applied analysis》 - 2025,24(1) - 60～83 - 共24页

摘要： stability of implicit differential-algebraic equations | with the leading term of derivatives to be singular | and the driving term to be a causal linear operator | . In this paper, we deal with the robust | . First, we consider the solvability of linear and

关键词： Quasilinear | differential-algebraic equation | causal operator | index | robust stability | robust stability.

8. A fast temporal second-order compact finite difference method for two-dimensional parabolic integro-differential equations with weakly singular kernel NSTL国家科技图书文献中心

Zheng, Zi-Yun | Wang, Yuan-Ming - 《Journal of computational science》 - 2025,87(May) - 1.1～1.18 - 共18页

摘要： twodimensional parabolic integro-differential* equations with* | weakly singular* kernel. The sum-of-exponentials* | weakly singular* integral term, and the fourth-order* | the spatial derivative operator. We use the discrete | spatial fourth-order convergence for weakly singular

关键词： Integro-differential equations | Weakly singular kernel | Compact finite difference method | Fast algorithm | Stability and convergence | ACCURATE NUMERICAL-METHOD | SPLINE COLLOCATION METHODS | EVOLUTION EQUATION | CONVOLUTION QUADRATURE | CRANK-NICOLSON...

9. A Note on Generalized Locally Toeplitz Operators NSTL国家科技图书文献中心

V. B. Kiran Kumar | N. S. Sarathkumar - 《Numerical linear algebra with applications》 - 2025,32(3) - n/a～n/a - 共18页

摘要： approximating Partial Differential* Equations (PDEs* | ), Fractional Differential* Equations (FDEs), and Integro* | ‐Differential* Equations (IDEs). These sequences are used to* | study the spectral and singular* value behavior of* | Discontinuous Galerkin methods. Spectral and singular* value*

关键词： generalized locally Toeplitz operator | generalized locally Toeplitz sequences | singular value and eigenvalue asymptotics

10. Existence results of non-local integro-differential problem with singularity under a new fractional Musielak-Sobolev space* NSTL国家科技图书文献中心

Cheng, Yu | Bai, Zhanbing - 《Journal of physics,A.Mathematical and theoretical》 - 2025,58(4) - 共28页

摘要：-differential* operators. The completeness, reflexivity, and* | class of non-local problems with singular | . Furthermore, we provide two concrete operator* examples* | In this article, we construct a new fractional | Musielak-Sobolev space designed to address the non

摘要： singular differential operator in the space L2(& Ropf | third-order differential* operator and demonstrate the* | solutions to the equation associated with the operator. We | and obtain two-sided bounds for the singular* numbers* | the resolvent of the operator* under consideration*

关键词： approximation numbers | completeness of root vectors | nuclearity | resolvent | separability | singular operator | third-order differential operator | third‐order differential operator

关键词： Quasi-interpolants operators | Fredholm integro-differential equations | Weakly singular kernel | Graded grids

摘要：In this paper, the derivative nonlinear | Schroedinger equations with Legendre potential i | |~2 _ = 0 subject to certain boundary | conditions was considered, where the potential function | ( ) = 1/2 1/4tan~2 , ( /2 , /2), has

关键词： Completely resonant | quasi-periodic solutions | KAM for PDE | singular differential operator | small divisors

摘要： singular differential operator in the principal part is | A linear integro-differential* equation with a* | studied. For its approximate solution in the space of | generalized functions, a special generalized version of the | collocation method is proposed and substantiated.

关键词： integro-differential equation | approximate solution | direct method | theoretical justification

摘要： by a nonlocal integro- differential* operator L-K:u* | In this paper, we investigate the following | fractional Kirchhoff-type pseudo parabolic equation driven | (s) + M([u](s)(2))L | (K)u + L (K)u(t) = vertical bar u vertical bar(p-2

关键词： blow-up | fractional parabolic problem of Kirchhoff type | logarithmic nonlinearity | nonlocal integro-differential operator | singular potential | blow‐up | nonlocal integro‐differential operator

摘要： operator. The singular term is not decoupled from the | We consider a singular* eigenvalue problem* | driven by a nonlinear nonhomogeneous differential | rest of the reaction, as is the case in most singular | elliptic problems. Using variational tools together with

关键词： Nonlinear nonhomogeneous differential operator | nonlinear regularity theory | truncation | positive solutions | Hardy's inequality

摘要： stability of implicit differential-algebraic equations | with the leading term of derivatives to be singular | and the driving term to be a causal linear operator | . In this paper, we deal with the robust | . First, we consider the solvability of linear and

关键词： Quasilinear | differential-algebraic equation | causal operator | index | robust stability | robust stability.

摘要： twodimensional parabolic integro-differential* equations with* | weakly singular* kernel. The sum-of-exponentials* | weakly singular* integral term, and the fourth-order* | the spatial derivative operator. We use the discrete | spatial fourth-order convergence for weakly singular

关键词： Integro-differential equations | Weakly singular kernel | Compact finite difference method | Fast algorithm | Stability and convergence | ACCURATE NUMERICAL-METHOD | SPLINE COLLOCATION METHODS | EVOLUTION EQUATION | CONVOLUTION QUADRATURE | CRANK-NICOLSON...

关键词： generalized locally Toeplitz operator | generalized locally Toeplitz sequences | singular value and eigenvalue asymptotics

摘要：-differential* operators. The completeness, reflexivity, and* | class of non-local problems with singular | . Furthermore, we provide two concrete operator* examples* | In this article, we construct a new fractional | Musielak-Sobolev space designed to address the non

关键词： fractional Musielak-Sobolev space | singularity | non-local operator | Nehari manifold

4008-161-200 800-990-8900

国家科技图书文献中心

摘要： singular differential operator in the space L2(& Ropf | third-order differential operator and demonstrate the | solutions to the equation associated with the operator. We | and obtain two-sided bounds for the singular numbers | the resolvent of the operator under consideration

关键词： approximation numbers | completeness of root vectors | nuclearity | resolvent | separability | singular operator | third-order differential operator | third‐order differential operator

摘要：-differential equation with weakly singular kernel. Also, some | -interpolant operator to numerically address a class of | linear integro-differential equations with weakly | singular kernel. As stated in Pedas and Tamme (2006), the | quasi-interpolant operator in this particular space

关键词： Quasi-interpolants operators | Fredholm integro-differential equations | Weakly singular kernel | Graded grids

摘要：In this paper, the derivative nonlinear | Schroedinger equations with Legendre potential i | |~2 _ = 0 subject to certain boundary | conditions was considered, where the potential function | ( ) = 1/2 1/4tan~2 , ( /2 , /2), has

关键词： Completely resonant | quasi-periodic solutions | KAM for PDE | singular differential operator | small divisors

摘要： singular differential operator in the principal part is | A linear integro-differential equation with a | studied. For its approximate solution in the space of | generalized functions, a special generalized version of the | collocation method is proposed and substantiated.

关键词： integro-differential equation | approximate solution | direct method | theoretical justification

摘要： by a nonlocal integro- differential operator L-K:u | In this paper, we investigate the following | fractional Kirchhoff-type pseudo parabolic equation driven | (s) + M([u](s)(2))L | (K)u + L (K)u(t) = vertical bar u vertical bar(p-2

关键词： blow-up | fractional parabolic problem of Kirchhoff type | logarithmic nonlinearity | nonlocal integro-differential operator | singular potential | blow‐up | nonlocal integro‐differential operator

摘要： operator. The singular term is not decoupled from the | We consider a singular eigenvalue problem | driven by a nonlinear nonhomogeneous differential | rest of the reaction, as is the case in most singular | elliptic problems. Using variational tools together with

关键词： Nonlinear nonhomogeneous differential operator | nonlinear regularity theory | truncation | positive solutions | Hardy's inequality

摘要： stability of implicit differential-algebraic equations | with the leading term of derivatives to be singular | and the driving term to be a causal linear operator | . In this paper, we deal with the robust | . First, we consider the solvability of linear and

关键词： Quasilinear | differential-algebraic equation | causal operator | index | robust stability | robust stability.

摘要： twodimensional parabolic integro-differential equations with | weakly singular kernel. The sum-of-exponentials | weakly singular integral term, and the fourth-order | the spatial derivative operator. We use the discrete | spatial fourth-order convergence for weakly singular

关键词： Integro-differential equations | Weakly singular kernel | Compact finite difference method | Fast algorithm | Stability and convergence | ACCURATE NUMERICAL-METHOD | SPLINE COLLOCATION METHODS | EVOLUTION EQUATION | CONVOLUTION QUADRATURE | CRANK-NICOLSON...

摘要： approximating Partial Differential Equations (PDEs | ), Fractional Differential Equations (FDEs), and Integro | ‐Differential Equations (IDEs). These sequences are used to | study the spectral and singular value behavior of | Discontinuous Galerkin methods. Spectral and singular value

关键词： generalized locally Toeplitz operator | generalized locally Toeplitz sequences | singular value and eigenvalue asymptotics

摘要：-differential operators. The completeness, reflexivity, and | class of non-local problems with singular | . Furthermore, we provide two concrete operator examples | In this article, we construct a new fractional | Musielak-Sobolev space designed to address the non

关键词： fractional Musielak-Sobolev space | singularity | non-local operator | Nehari manifold

4008-161-200 800-990-8900

国家科技图书文献中心

摘要： singular differential operator in the space L2(& Ropf | third-order differential* operator and demonstrate the* | solutions to the equation associated with the operator. We | and obtain two-sided bounds for the singular* numbers* | the resolvent of the operator* under consideration*

摘要： singular differential operator in the principal part is | A linear integro-differential* equation with a* | studied. For its approximate solution in the space of | generalized functions, a special generalized version of the | collocation method is proposed and substantiated.

摘要： by a nonlocal integro- differential* operator L-K:u* | In this paper, we investigate the following | fractional Kirchhoff-type pseudo parabolic equation driven | (s) + M([u](s)(2))L | (K)u + L (K)u(t) = vertical bar u vertical bar(p-2

摘要： operator. The singular term is not decoupled from the | We consider a singular* eigenvalue problem* | driven by a nonlinear nonhomogeneous differential | rest of the reaction, as is the case in most singular | elliptic problems. Using variational tools together with

摘要： twodimensional parabolic integro-differential* equations with* | weakly singular* kernel. The sum-of-exponentials* | weakly singular* integral term, and the fourth-order* | the spatial derivative operator. We use the discrete | spatial fourth-order convergence for weakly singular

摘要：-differential* operators. The completeness, reflexivity, and* | class of non-local problems with singular | . Furthermore, we provide two concrete operator* examples* | In this article, we construct a new fractional | Musielak-Sobolev space designed to address the non