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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