## Topological Methods in Nonlinear Analysis

### Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction

#### Abstract

We consider a parametric semilinear Dirichlet problem driven by the Laplacian plus an indefinite unbounded potential and with a reaction of superdifissive type. Using variational and truncation techniques, we show that there exists a critical parameter value $\lambda_{\ast} > 0$ such that for all $\lambda > \lambda_{\ast}$ the problem has at least two positive solutions, for $\lambda= \lambda_{\ast}$ the problem has at least one positive solution, and no positive solutions exist when $\lambda\in(0,\lambda_{\ast})$. Also, we show that for $\lambda\geq\lambda_{\ast}$ the problem has a smallest positive solution.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 2 (2016), 423-438.

Dates
First available in Project Euclid: 13 July 2016

https://projecteuclid.org/euclid.tmna/1468413746

Digital Object Identifier
doi:10.12775/TMNA.2016.014

Mathematical Reviews number (MathSciNet)
MR3559915

Zentralblatt MATH identifier
1362.35118

#### Citation

Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile. Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction. Topol. Methods Nonlinear Anal. 47 (2016), no. 2, 423--438. doi:10.12775/TMNA.2016.014. https://projecteuclid.org/euclid.tmna/1468413746

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