Symmetric positive solutions for $\phi$-Laplacian boundary-value problems with integral boundary conditions

Abstract

In this article, we study the existence, multiplicity, and nonexistence of symmetric positive solutions for a class of four-order integral boundary value problems with $\phi$-Laplacian operator. The arguments mainly rely on the Guo-Krasnosel'skii fixed point theorem of cone expansion and compression of norm type and Leggett-Williams fixed point theorem. Finally, some examples are presented to illustrate the main results.

Keywords

• Boundary value problems
• integral boundary conditions
• symmetric positive solutions
• \phi-Laplacian operator
• fixed point theorem