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

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