Differential and Integral Equations

On pairs of positive solutions for a class of quasilinear elliptic problems

Lynnyngs Kelly Arruda and Ilma Marques

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We prove, by using bifurcation theory, the existence of at least two positive solutions for the quasilinear problem $-\Delta_p u = f(x,u)$ in $\Omega$, $u=0$ on $\partial \Omega$, where $N>p>1$ and $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $N\geq2,$ and the non-linearity $f$ is a locally Lipschitz continuous function, among other assumptions.

Article information

Differential Integral Equations, Volume 22, Number 5/6 (2009), 575-585.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J92: Quasilinear elliptic equations with p-Laplacian
Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35J25: Boundary value problems for second-order elliptic equations


Arruda, Lynnyngs Kelly; Marques, Ilma. On pairs of positive solutions for a class of quasilinear elliptic problems. Differential Integral Equations 22 (2009), no. 5/6, 575--585. https://projecteuclid.org/euclid.die/1356019607

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