On the fractional p-Laplacian problems

Abstract

Abstract This paper deals with nonlocal fractional p-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractional p-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next show that there exists a limit sequence of a sequence of weak solutions for finite-dimensional problems, and this limit sequence is a sequence of the solutions of our problems. We get this result by the estimate of the energy functional and the compactness property of continuous embedding inclusions between some special spaces.

Keywords

• Nonlocal fractional p-Laplacian problems with difference
• Fractional Laplace space
• Fractional Sobolev space
• Approximation method
• Approximation weak solution
• Limit sequence of the approximation weak solutions