Weak Solutions and Riesz Expansion for Impulsive Boundary Value Problems

Year 2025, Issue: 53, 77 - 86, 31.12.2025

Hayati Olğar

https://doi.org/10.53570/jnt.1799207

Abstract

In this paper, some spectral properties of the eigenvalues and generalized eigenfunctions of a many-interval boundary-value-jump problem (MIBVJP), which consists of a second-order differential equation defined on a finite number of disjoint intervals under supplementary impulsive conditions and $\lambda$-dependent boundary conditions. Using the theory of operator polynomials in Sobolev space and suitable integral transformations, the basis property of generalized eigenfunctions for the MIBVJP is obtained, and positive definiteness and self-adjointness of the operator polynomial are involved.

Keywords

Boundary value problems , eigenvalues , eigenfunctions , generalized eigenfunctions , Riesz basis

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