On the Fredholm alternative for the \(p\)-Laplacian
type: Item
instance of: scholarly article
title: On the Fredholm alternative for the \(p\)-Laplacian
zbMATH Open document ID: 1058.34019
DOI: 10.1016/S0096-3003(03)00653-2
author: Xiaojing Yang
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: The author deals with the boundary value problem \[ (p-1)^{-1} ((\varphi_p(u'))'+ \alpha\varphi_p (u^+)- \beta\varphi_p (u^-))= f(\varphi_p(u))+ h(t) \text{ in }(0,T), \quad u(0)= u(T)= 0, \] where \(p>1\), \(\varphi_p(u)=| u|^{p-2}u\), \(T= (p-1)^{1/p} \alpha^{-1/p} \pi_p\), \(\pi_p= \frac {2\pi}{p}\sin (\frac \pi p)\), \(h\in L^\infty (0,T)\), \(f\in C(\mathbb{R}, \mathbb{R})\) is bounded, \(\lim_{x\to+\infty} f(x)= f(+\infty)\) exists, \(\alpha>0\), \(\beta>0\) and \((p-1)^{1/p} (\alpha^{-1/p}+ \beta^{-1/p})= 2\). To this end the author uses a generalized polar coordinates transformation and the methods of nonlinear functional analysis.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2082070
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: Fredholm alternative
zbMATH Keywords: Leray-Schauder degree
zbMATH Keywords: generalized polar coordinates
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: The Fredholm alternative at the first eigenvalue for the one dimensional \(p\)-Laplacian
cites work: A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
cites work: Multiple Solutions for the p-Laplacian Under Global Nonresonance
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cites work: On the Fredholm alternative for the $p$-Laplacian
cites work: Bifurcation Phenomena Associated to the p-Laplace Operator
cites work: On the closed solution to some nonhomogeneous eigenvalue problem with \(p\)-Laplacian
full work available at URL: s0096-3003(03)00653-2
OpenAlex ID: W2021991815
description: scientific article; zbMATH DE number 2082070