# zbMATH — the first resource for mathematics

Positive solutions of some nonlinear elliptic problems in unbounded domain. (English) Zbl 1136.35369
Summary: We study the existence of positive solutions of the nonlinear elliptic equation $$\Delta u+\varphi(\cdot,u)=0$$, in an unbounded domain $$D$$ in $$\mathbb R^n$$, $$n\geq 3$$, with compact boundary. Our purpose is to give some existence results for the above equation with some boundary values, where the nonlinear term $$\varphi(t,x)$$ satisfies some appropriate conditions related to a certain Kato class $$K^\infty(D)$$. We give also some estimates on the solution $$u$$.

##### MSC:
 35J60 Nonlinear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
Full Text: