Existence of solutions for semilinear elliptic equations with indefinite linear part. (English) Zbl 0766.35009

The equations of the type \((-\Delta+V-\lambda)u=W(x)| u|^{p-2} u\), \((-\Delta+V-\lambda)u=f(u)\), where \(V\in L(\mathbb{R}^ N)\), \(\lambda\not\in\sigma(-\Delta+V)\) are considered. It is supposed that \(W(x)\in L^ \infty(\mathbb{R}^ n)\), \(W(x)\to0\) as \(| x|\to+\infty\), \(f(u)\) is an odd strictly increasing continuous function, which has superlinear but subcritical bounds. Introducing energy functionals and using dual variational methods some existence results are proved. An interesting point is the using of variational analysis of functionals on the Orlicz space \(L_ G\).
Reviewer: S.Tersian (Russe)


35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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