## A multiplicity result for a class of superlinear elliptic problems.(English)Zbl 0814.35038

Summary: We prove the existence of at least two solutions for a superlinear problem $$-\Delta u = \Phi (x,u) + \tau e_ 1$$ $$(u \in H^ 1_ 0 (\Omega))$$ and $$e_ 1$$ is the first eigenvector of $$(-\Delta, H^ 1_ 0(\Omega))$$, when $$\tau$$ is large enough, if $$\Phi \in C(\mathbb{R}, \mathbb{R})$$ and $$\Phi (x,s) = g(x,s) + h(x,s)$$ where $$h$$ is a superlinear nonlinearity with a suitable growth at $$+ \infty$$ and $$g$$ is asymptotically linear.

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations 35J60 Nonlinear elliptic equations

### Keywords:

semilinear elliptic equation; superlinear nonlinearity
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