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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
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