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.
Citation
Sergiu Aizicovici. Nikolaos S. Papageorgiou. Vasile Staicu. "Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction." Topol. Methods Nonlinear Anal. 47 (2) 423 - 438, 2016. https://doi.org/10.12775/TMNA.2016.014
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