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

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.

MSC:

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