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

Alama, Stanley; Li, YanYan

J. Differ. Equations 96, No. 1, 89-115 (1992).

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)

MSC:

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

Keywords:

Schrödinger operator; mountain pass theorem; energy functionals; variational methods; Orlicz space

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