## Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains.(English)Zbl 1189.35132

Summary: We prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem
$Lu-\mu ug_1+ h(u)g_2= f\quad \text{in }\Omega,\qquad u = 0\quad \text{on }\partial\Omega$
in a suitable weighted Sobolev space. Here the domain $$\Omega\subset\mathbb R^n$$, $$n\geq 3$$, is not necessarily bounded, and $$h$$ is a continuous bounded nonlinearity. The theory is also extended for $$h$$ continuous and unbounded.

### MSC:

 35J70 Degenerate elliptic equations 35J61 Semilinear elliptic equations 35D30 Weak solutions to PDEs 35J25 Boundary value problems for second-order elliptic equations
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