Positive solutions for generalized nonlinear logistic equations of superdiffusive type
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Generalized p-logistic equation, superdiffusive case, p-Laplacian, nonlinear maximum principle, positive solution, comparison theoremAbstrakt
We consider a generalized version of the $p$-logistic equation. Using variational methods based on the critical point theory and truncation techniques, we prove a bifurcation-type theorem for the equation. So, we show that there is a critical value $\lambda_*> 0$ of the parameter $\lambda> 0$ such that the following holds: if $\lambda> \lambda_*$, then the problem has two positive solutions; if $\lambda=\lambda_*$, then there is a positive solution; and finally, if $0< \lambda< \lambda_*$, then there are no positive solutions.Pobrania
Opublikowane
2011-04-23
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IANNIZZOTTO, Antonio & PAPAGEORGIOU, Nikolaos S. Positive solutions for generalized nonlinear logistic equations of superdiffusive type. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2011, T. 38, nr 1, s. 95–113. [udostępniono 22.7.2024].
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