Abstract
In this paper, we investigate the existence of solutions for the fractional p-Laplace equation (−Δ)psu+V(x)|u|p−2u=h1(x)|u|q−2u+h2(x)|u|r−2uin RN,\\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}$$ (-\\Delta)_{p}^{s}u+V(x) \\vert u \\vert ^{p-2}u=h_{1}(x) \\vert u \\vert ^{q-2}u+h_{2}(x) \\vert u \\vert ^{r-2}u \\quad \\mbox{in } \\mathbb{R}^{N}, $$\\end{document} where N>sp, 0< s<1<p, 1< q< p< r< p_{s}^{*}:=frac{Np}{N-sp}, and the potential function V(x)>0 and h_{1}(x), h_{2}(x) are allowed to change sign in mathbb {R}^{N}. By using variant fountain theorem, we prove that the above equation admits infinitely many small and high energy solutions.
Highlights
Introduction and main resultIn this paper, we consider the existence and multiplicity of solutions for the following elliptic problem:(– )spu + V (x)|u|p–2u = h1(x)|u|q–2u + h2(x)|u|r–2u in RN, (1.1)where (– )sp is the fractional p-Laplacian operator with 0 < s < 1 < p and sp < N, 1 < q < 0, h1 and h2 are sign-changing weight functions
In this paper, we investigate the existence of solutions for the fractional p-Laplace equation
By using variant fountain theorem, we prove that the above equation admits infinitely many small and high energy solutions
Summary
By using variant fountain theorem, we prove that the above equation admits infinitely many small and high energy solutions. 1 Introduction and main result In this paper, we consider the existence and multiplicity of solutions for the following elliptic problem: (– )spu + V (x)|u|p–2u = h1(x)|u|q–2u + h2(x)|u|r–2u in RN , (1.1)
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