Abstract
In the present paper, we prove the existence of at least three radial solutions of the p-Laplacian problem with nonlinear gradient term {Δpv+f(|x|,v,|∇v|)=0in Ω,v=0on ∂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}$$\\textstyle\\begin{cases} \\Delta_{p}v+f(\\vert x\\vert ,v,\\vert \\nabla v\\vert )=0\\quad \\mbox{in }\\Omega, \\\\ v=0\\quad \\mbox{on }\\partial\\Omega, \\end{cases} $$\\end{document} and the corresponding one-parameter problem. Here Ω is a unit ball in mathbb{R}^{N}. Our approach relies on the Avery-Peterson fixed point theorem. In contrast with the usual hypotheses, no asymptotic behavior is assumed on the nonlinearity f with respect to phi_{p}(cdot).
Highlights
1 Introduction In the present paper, we are concerned with the multiplicity of positive radial solutions to the quasilinear elliptic p-Laplacian problem with nonlinear gradient term
The elliptic p-Laplacian problems with nonlinear gradient term have been extensively studied via different methods [ – ], for example, critical point theory, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, sub- and supersolutions, and so on
By applying the Schauder fixed point theorem and suband supersolutions, the authors showed that problem ( . ) has a positive solution
Summary
Introduction In the present paper, we are concerned with the multiplicity of positive radial solutions to the quasilinear elliptic p-Laplacian problem with nonlinear gradient term By applying the Schauder fixed point theorem and suband supersolutions, the authors showed that problem
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