MULTIPLICITY RESULTS TO A FOURTH-ORDER BOUNDARY VALUE PROBLEM FOR A STURM-LIOUVILLE TYPE EQUATION

Year 2020, Volume: 10 Issue: 1, 69 - 80, 01.01.2020

A. Ghazvehi G. A. Afraouzi

Abstract

We establish the existence of at least three distinct weak solutions for a fourth-order Sturm-Liouville type problem under appropriate hypotheses. Our main tools are based on variational methods and some critical points theorems. Moreover, when the energy functional is not coercive, an existence result of two distinct solutions is given. We give some examples to illustrate the obtained results.

Keywords

Fourth-order boundary value problem, Sturm-Liouville type problem, three solutions, variational methods.

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• Ahmad Ghazvehi is a Ph.D. student (since 2014) in Department of Mathemat- ics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
• He works on nonlinear analysis, nonlinear functional analysis theory of differential equations and applied functional analysis. Ghasem Alizadeh Afrouzi is a member in Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran, since 1989.
• His current research interests are nonlinear analysis, theory of Differential equations, Applied functional Analysis, nonlinear functional Analysis, and calculus of Variations.