SOLVABILITY OF A RESONANT FRACTIONAL-ORDER p-LAPLACIAN BOUNDARY VALUE PROBLEM WITH TWO-DIMENSIONAL KERNEL

SOLVABILITY OF A RESONANT FRACTIONAL-ORDER p-LAPLACIAN BOUNDARY VALUE PROBLEM WITH TWO-DIMENSIONAL KERNEL

M. Azouzi, E. Zeraoulia, L. Guedda

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Abstract

The goal of this study is to establish the existence of solutions for a fractional- order p-Laplacian boundary value problem with a two-dimensional kernel at resonance case. The non-linearity of this problem forced us to transform it into a semilinear system to use the so called Mawhin's coincidence degree theory. In addition, an example is included to demonstrate the main result.

Keywords

Fractional-order p-Laplacian, Resonance case, Semilinear system, Mawhin's coincidence degree theory.