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H. Guggenheimer 《Annali di Matematica Pura ed Applicata》1974,98(1):281-296
Sunto Il limite inferiore classico per i valori propri di una equazione differenziale lineare del secondo ordine nel caso dei punti
coniugati è un caso speciale di disuguaglianze per problemi auto-aggiunti generali. Per equazioni auto-aggiunte a coefficiente
positivo e parametro moltiplicativo possiamo determinare il segno dei valori propri ed otteniamo una serie completa di limiti
inferiori, con esempi nei quali i limiti sono raggiunti. Si mostra che, senza ipotesi speciali sul coefficiente, esistono
limiti superiori soltanto per qualche caso del vaiore proprw d'ordine zero. Anche questi limiti sono raggiunti in esempi.
Dedicated to ProfessorBeniamino Segre
Entrata in Redazione il 12 Febbraio 1973.
Research partially supported by NSF Grant GP-27960. 相似文献
Dedicated to ProfessorBeniamino Segre
Entrata in Redazione il 12 Febbraio 1973.
Research partially supported by NSF Grant GP-27960. 相似文献
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B. Pelloni 《Journal of Computational and Applied Mathematics》2010,234(6):1685-1691
We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework. 相似文献
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Multiplicity results for Sturm–Liouville boundary value problems are obtained. Proofs are based on variational methods. 相似文献
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Giuseppina D'Aguì Beatrice Di Bella Stepan Tersian 《Mathematical Methods in the Applied Sciences》2016,39(5):1060-1068
We study the existence and multiplicity of solutions for a nonlinear boundary value problem subject to perturbations of impulsive terms. Under suitable assumptions on the potential of the nonlinearity, the existence of one or two solutions is established. Our approach is based on a local minimum theorem and a two non‐zero critical points for differentiable functionals. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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T. S. Angell R. E. Kleinman G. C. Hsiao 《Mathematical Methods in the Applied Sciences》1982,4(1):164-193
In this paper we study the application of boundary integral equation methods for the solution of the third, or Robin, boundary value problem for the exterior Helmholtz equation. In contrast to earlier work, the boundary value problem is interpreted here in a weak sense which allows data to be specified in L∞ (?D), ?D being the boundary of the exterior domain which we assume to be Lyapunov of index 1. For this exterior boundary value problem, we employ Green's theorem to derive a pair of boundary integral equations which have a unique simultaneous solution. We then show that this solution yields a solution of the original exterior boundary value problem. 相似文献
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E. H. Khalilov 《Computational Mathematics and Mathematical Physics》2016,56(7):1310-1318
The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined. 相似文献
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S. Engleder 《Journal of Mathematical Analysis and Applications》2007,331(1):396-407
In this paper we describe some modified regularized boundary integral equations to solve the exterior boundary value problem for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. We formulate combined boundary integral equations which are uniquely solvable for all wave numbers even for Lipschitz boundaries Γ=∂Ω. This approach extends and unifies existing regularized combined boundary integral formulations. 相似文献
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We investigate the existence of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem on ; on , where is a bounded region in , is an indefinite weight function and may be positive, negative or zero.
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The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green’s function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012). 相似文献
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Yunmei Chen 《偏微分方程通讯》2013,38(1-2):101-124
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Xian Xu 《Journal of Mathematical Analysis and Applications》2004,291(2):673-689
In this paper, some multiplicity results for positive solutions of some singular semi-positone three-point boundary value problem be obtained by using the fixed point index method. 相似文献
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In this paper we study a class of boundary value problems with impulsive effects. Under some natural assumptions, by using Morse theory in combination with the minimax arguments, we establish some new results on the existence of multiple nontrivial solutions for the problems. Recent results from the literature are improved and extended. 相似文献