## 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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### References:

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