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Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques. (English) Zbl 1164.35341
Summary: A class of semilinear elliptic equations with dependence on the gradient is considered. The existence of a positive and a negative solution is stated through an iterative method based on mountain-pass techniques.

MSC:
35J61Semilinear elliptic equations
35J20Second order elliptic equations, variational methods
35J25Second order elliptic equations, boundary value problems
47J30Variational methods (nonlinear operator equations)
58E05Abstract critical point theory