in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if uln is an eigenfunction associated with the nth variational eigenvalue, ln, then uln has at most 2n−2 nodal domains. Also, if uln has n+k nodal domains, then there is another eigenfunction with at most n−k nodal domains. © 2002 Elsev...

We are interested in a nonlinear boundary value problem for (|u′′|p−2u′′)′′ = λ|u|p−2u in [0,1], p > 1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the nth eigenvalue, has precisely n− 1 zero points in (0,1). Eigenvalues of the ...

The article describes the eigenvalue and eigenfunction problems. Basic properties, some applications and examples in system analysis are provided.

A method for simultaneously approximating to high accuracy the corresponding eigenvalue and zeros of the (n + l)st eigenfunction of a regular Sturm-Liouville eigenvalue problem is presented. It is based upon equilibrating the minimum eigenvalues of several problems on subintervals that form a partition of the orginal interval. The method is easily derived from classical mini-max variational pri...

Abstract We derive optimal and asymptotically exact a posteriori error estimates for the approximation of eigenfunction Laplace eigenvalue problem. To do so, we combine two results from literature. First, use hypercircle techniques developed mixed approximations with Raviart-Thomas finite elements. In addition, post-processings introduced based on Brezzi-Douglas-Marini element. these approaches...

A modiied deenition of a-eigenvalue is introduced where is a nonnegative measure in the local Kato class. Dependence of the-eigenvalues of ?4+, where is a positive measure on the domain and on the measure are investigated. It is also proved that the smallest-eigenvalue is non degenerate with positive associated-eigenfunction.