Differential and Integral Equations

Multiple nontrivial solutions for $p$-Laplacian equations with an asymmetric nonlinearity

Shouchuan Hu and Nikolaos S. Papageorgiou

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In this paper we study a nonlinear Dirichlet problem driven by the p-Laplacian and a right-hand side nonlinearity which exhibits an asymmetric behavior near $+ \infty$ and $- \infty$. Using variational techniques based on the mountain pass theorem and the second deformation theorem, we prove the existence of at least two nontrivial $C^1$- solutions, one of which is strictly positive.

Article information

Differential Integral Equations, Volume 19, Number 12 (2006), 1371-1390.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations 47J30: Variational methods [See also 58Exx]


Hu, Shouchuan; Papageorgiou, Nikolaos S. Multiple nontrivial solutions for $p$-Laplacian equations with an asymmetric nonlinearity. Differential Integral Equations 19 (2006), no. 12, 1371--1390. https://projecteuclid.org/euclid.die/1356050294

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