共查询到20条相似文献,搜索用时 15 毫秒
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We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues
and eigenfunctions of the problems asm→−0.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999. 相似文献
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We consider a simply supported beam with restoring and external forces given as a sum of a continuous function and a Dirac delta distribution. We present sufficient conditions on these data in order to guarantee a unique positive or negative solution, respectively. 相似文献
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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
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We study the existence of positive solutions of second-order ordinary differential equations with integral boundary conditions. The result generalizes the conditions obtained in [1] for the existence of positive solutions. 相似文献
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Ziyatkhan S. Aliyev Yagut N. Aliyeva 《Mathematical Methods in the Applied Sciences》2023,46(1):1282-1294
This paper is devoted to the study of global bifurcation from infinity of nontrivial solutions of a nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. We prove the existence of two families of unbounded continua of nontrivial solutions to this problem, which emanate from bifurcation points in and possess oscillatory properties of eigenfunctions (and their derivatives) of the corresponding linear problem in some neighborhoods of these bifurcation points. 相似文献
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In this paper, we consider a fourth-order boundary value problem with impulse. First, we establish criteria for the existence of one or more than one positive solution of a non-eigenvalue problem. Second, we are concerned with determining values of λ, for which there exist positive solutions for an eigenvalue problem. In both problems, we shall use the Krasnoselskii fixed point theorem. 相似文献
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R. Ch. Kulaev 《Differential Equations》2016,52(3):316-326
We study the spectral properties of a multipoint boundary value problem for a fourth-order equation that describes small deformations of a chain of rigidly connected rods with elastic supports. We study the dependence of the spectrum of the boundary value problem on the rigidity coefficients of the supports. We show that the spectrum of the boundary value problem splits into two parts, one of which is movable under changes of the rigidity coefficients and the other remains fixed. As the rigidity coefficients grow, the eigenvalues corresponding to the movable part of the spectrum grow as well; moreover, the double degeneration of some eigenvalues is possible. 相似文献
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