Micheletti, Anna Maria; Pistoia, Angela A multiplicity result for a class of superlinear elliptic problems. (English) Zbl 0814.35038 Port. Math. 51, No. 2, 219-229 (1994). 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. Cited in 2 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35J60 Nonlinear elliptic equations Keywords:semilinear elliptic equation; superlinear nonlinearity PDFBibTeX XMLCite \textit{A. M. Micheletti} and \textit{A. Pistoia}, Port. Math. 51, No. 2, 219--229 (1994; Zbl 0814.35038) Full Text: EuDML