共查询到20条相似文献,搜索用时 0 毫秒
1.
Paul A. Binding Patrick J. Browne Bruce A. Watson 《Journal of Mathematical Analysis and Applications》2004,291(1):246-261
Three inverse problems for a Sturm-Liouville boundary value problem −y″+qy=λy, y(0)cosα=y′(0)sinα and y′(1)=f(λ)y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different values of α or by the Prüfer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation. 相似文献
2.
Warren J. Code 《Journal of Mathematical Analysis and Applications》2005,309(2):729-742
We study Sturm-Liouville problems with right-hand boundary conditions depending on the spectral parameter in a quadratic manner. A modified Crum-Darboux transformation is used to produce chains of problems almost isospectral with the given one. The problems in the chain have boundary conditions which in various cases are affine or bilinear in the spectral parameter, and in all cases culminate in a problem with constant boundary conditions. This extends recent work of Binding, Browne, Code and Watson when the right-hand condition is either an affine function of the spectral parameter with negative leading coefficient or a Herglotz function. 相似文献
3.
Zhan Zhou 《Journal of Differential Equations》2010,249(5):1199-5507
In this paper, we obtain a new sufficient condition on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems by using critical point theory in combination with periodic approximations. We prove that it is also necessary in some special cases. 相似文献
4.
This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories. 相似文献
5.
Elgiz Bairamov Yelda Aygar Turhan Koprubasi 《Journal of Computational and Applied Mathematics》2011,235(16):4519-4523
Let us consider the boundary value problem (BVP) for the discrete Sturm-Liouville equation
6.
Second-order nonlinear singular Sturm-Liouville problems with integral boundary conditions 总被引:1,自引:0,他引:1
This paper is concerned with the second-order singular Sturm-Liouville integral boundary value problems
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Betty Jean Harmsen 《Journal of Difference Equations and Applications》2013,19(7):639-653
This paper deals with discrete second order Sturm-Liouville problems where the parameter that is part of the Sturm-Liouville difference equation appears nonlinearly in the boundary conditions. The operator is extended to a self-adjoint operator and an expansion theorem is proved. 相似文献
11.
Huaqing Sun 《Linear algebra and its applications》2006,414(1):361-372
This paper is concerned with coupled boundary value problems for self-adjoint second-order difference equations. Existence of eigenvalues is proved, numbers of eigenvalues are calculated, and relationships between the eigenvalues of a self-adjoint second-order difference equation with three different coupled boundary conditions are established. These results extend the relevant existing results of periodic and antiperiodic boundary value problems. 相似文献
12.
Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay
The existence of periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay is obtained by using stability properties of a bounded solution. 相似文献
13.
The boundary value problem for second order difference equation
14.
We study a nonlinear eigenvalue problem for a Sturm-Liouville operator on the interval (0, 1). The boundary conditions posed
at both endpoints of the interval depend on the spectral parameter. We prove that the problem has an eigenfunction system
that is a basis in the space L
p
(0, 1) for p > 1 and a Riesz basis for p = 2. 相似文献
15.
In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with the boundary value transmission problems on the suitable Hilbert spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which are established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces. 相似文献
16.
Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh–Weyl theorem, Hochstadt–Lieberman theorem and Mochizuki–Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm–Liouville operator on a finite interval. 相似文献
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In this paper, some sufficient conditions for the existence of solutions to the boundary value problems of a class of second order difference equation are obtained by using the critical point theory. 相似文献
19.
Călin-Ioan Gheorghiu 《Numerical Algorithms》2018,77(1):77-93
In this paper, we consider the numerical treatment of singular eigenvalue problems supplied with eigenparameter dependent boundary conditions using spectral methods. On the one hand, such boundary conditions hinder the construction of test and trial space functions which could incorporate them and thus providing well-conditioned Galerkin discretization matrices. On the other hand, they can generate surprising behavior of the eigenvectors hardly detected by analytic methods. These singular problems are often indirectly approximated by regular ones. We argue that spectral collocation as well as tau method offer remedies for the first two issues and provide direct and efficient treatment to such problems. On a finite domain, we consider the so-called Petterson-König’s rod eigenvalue problem and on the half line, we take into account the Charney’s baroclinic stability problem and the Fourier eigenvalue problem. One boundary condition in these problems depends on the eigenparameter and additionally, this also could depend on some physical parameters. The Chebyshev collocation based on both, square and rectangular differentiation and a Chebyshev tau method are used to discretize the first problem. All these schemes cast the problems into singular algebraic generalized eigenvalue ones which are solved by the QZ and/or Arnoldi algorithms as well as by some target oriented Jacobi-Davidson methods. Thus, the spurious eigenvalues are completely eliminated. The accuracy of square Chebyshev collocation is roughly estimated and its order of approximation with respect to the eigenvalue of interest is determined. For the problems defined on the half line, we make use of the Laguerre-Gauss-Radau collocation. The method proved to be reliable, accurate, and stable with respect to the order of approximation and the scaling parameter. 相似文献
20.
In this paper, the existence, multiplicity, and nonexistence results of nontrivial solutions are obtained for discrete nonlinear fourth-order boundary value problems with three parameters. The methods used here are based on the critical point theory and monotone operator theory. 相似文献