A Multiplicity Result for a Class of Superlinear Elliptic Problems

Anna Maria Micheletti and Angela Pistoia

Abstract: 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 $\Phi \in C(\R , \R )$ 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.

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