Differential and Integral Equations

A note on multiple solutions for sublinear elliptic systems

Miguel Ramos

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We prove the existence of a sequence of solutions approaching zero for an elliptic system of the form $-\Delta u=|v|^{q-2}v+g(x,v)$, $-\Delta v=|u|^{p-2}u+f(x,u)$ in a bounded domain, under Dirichlet homogeneous boundary conditions. We assume that $1 <p,q <2$ and that both $f(x,u)$ and $g(x,v)$ are small enough near the origin.

Article information

Differential Integral Equations, Volume 22, Number 9/10 (2009), 901-911.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly- Laplacian
Secondary: 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Ramos, Miguel. A note on multiple solutions for sublinear elliptic systems. Differential Integral Equations 22 (2009), no. 9/10, 901--911. https://projecteuclid.org/euclid.die/1356019514

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