Positive mountain pass solutions for a semilinear elliptic equation with a sign-changing weight function. (English) Zbl 1208.35056

Afrouzi, G. A.; Brown, K. J.

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 3, 409-416 (2006).

The authors extend previous results concerning the existence of positive solutions of the semilinear equation \(-\Delta u=\lambda gu(1-u)\) with homogeneous Dirichlet boundary condition on a bounded domain \(\Omega\), where \(\lambda>0\) and g is a smooth weight function on \(\Omega\), to the case where \(g\) changes sign. The approach relies on the mountain path theorem.

Reviewer: Dumitru Motreanu (Perpignan)

MSC:

35J61	Semilinear elliptic equations
35J20	Variational methods for second-order elliptic equations
35J25	Boundary value problems for second-order elliptic equations

Keywords:

semilinear elliptic equation; variational method; mountain path theorem; positive solutions

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