On some spectral properties of nonlocal boundary-value problems for nonlinear differential inclusion

Hameda Mohamed Alama

doi:10.3842/umzh.v76i10.7772

Hameda Mohamed Alama Department of Mathematics, Faculty of Science, Alasmarya Islamic University, Libya

DOI: https://doi.org/10.3842/umzh.v76i10.7772

Keywords: nonlinear differential inclusion; homogeneous and nonhomogeneous problem; Sturm-Liouville boundary value problem; nonlocal conditions; eigenvalues; eigenfunctions

Abstract

UDC 517.9

We study the solutions to the Sturm–Liouville boundary-value problem for a nonlinear differential inclusion with nonlocal conditions. The maximal and minimal solutions are demonstrated. The analysis of eigenvalues and eigenfunctions is performed. It is discussed whether multiple solutions may exist for the inhomogeneous Sturm–Liouville boundary-value problem for differential equation with nonlocal conditions.

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