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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 \(u\).

35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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