Abstract
In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following \t\t\tLKpu=λf(x,u)in Ω,u=0in RN∖Ω,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\begin{aligned} &\\mathcal{L}^{p}_{K}u=\\lambda f(x,u)&&\\text{in }\\Omega, \\\\ &u=0&&\\text{in }\\mathbb{R}^{N}\\setminus\\Omega, \\end{aligned} $$\\end{document} where mathcal{L}^{p}_{K} is a nonlocal operator with singular kernel, Ω is an open bounded smooth domain of mathbb{R}^{N}. Our purpose is to generalize the known results for fractional Laplacian equations to fractional p-Laplacian equations.
Highlights
1 Introduction Recently, a great attention has been devoted to the research of problems involving fractional and nonlocal operators
In this paper we deal with the following fractional problem in a bounded smooth domain ⊂ RN : ( . )
In Section, in a suitably chosen framework, we verify that the conditions in the abstract critical point theorems in [ ] are satisfied, we generalize the existence of multiplicity solutions for fractional Laplacian problems to the one for fractional p-Laplacian problems
Summary
A great attention has been devoted to the research of problems involving fractional and nonlocal operators. LpK is a nonlocal fractional operator defined as follows: LpK In Section , in a suitably chosen framework, we verify that the conditions in the abstract critical point theorems in [ ] are satisfied, we generalize the existence of multiplicity solutions for fractional Laplacian problems to the one for fractional p-Laplacian problems.
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