Nodal solutions to a class of nonstandard superlinear equations on \(\mathbb R^ N\). (English) Zbl 1126.35316

Conti, Monica; Terracini, Susanna; Verzini, Gianmaria

Adv. Differ. Equ. 7, No. 3, 297-318 (2002).

Summary: We investigate the existence of sign-changing radial solutions for a class of singular solutions of the form \[ -\Delta u(x)+b(| x| )u(x)=| u(x)| ^{\theta-1}u(x)+h(| x| ),\quad x\in\mathbb R^N, \] where \(b(| x| )\) may change sign and behaves like \(| x|^{-\alpha}\) at infinity for some \(\alpha\in(0,2)\), and \(\theta>1\).

MSC:

35J60	Nonlinear elliptic equations
34B15	Nonlinear boundary value problems for ordinary differential equations
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
47J30	Variational methods involving nonlinear operators
58E99	Variational problems in infinite-dimensional spaces

Keywords:

existence of sign-changing radial solutions