## Existence of three nontrivial solutions for an elliptic system.(English)Zbl 1159.35334

Summary: We consider the existence of nontrivial solutions for an elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones $$K_1,K_2\subset C(\overline{\Omega})$$ and computing the fixed point index in $$K_1$$, $$K_2$$ and $$K_1\times K_2$$, we obtain that the elliptic system has three nontrivial solutions $$(u,0)$$, $$(0,v)$$ and $$(u^*,v^*)$$. It is remarkable that the third nontrivial solution $$(u^*,v^*)$$ is established on the Cartesian product of two cones, in which the feature of two equations can be exploited better.

### MSC:

 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35J50 Variational methods for elliptic systems 35D05 Existence of generalized solutions of PDE (MSC2000)
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### References:

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