×

zbMATH — the first resource for mathematics

A note on multiple solutions for sublinear elliptic systems. (English) Zbl 1240.35204
Summary: 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.
MSC:
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J50 Variational methods for elliptic systems
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
PDF BibTeX XML Cite