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- W4299596004 abstract "We study the following boundary value problem with a concave-convex nonlinearity: begin{equation*} left{ begin{array}{r c l l} -Delta_p u & = & Lambda,u^{q-1}+ u^{r-1} & textrm{in }Omega, u & = & 0 & textrm{on }partialOmega. end{array}right. end{equation*} Here $Omega subset mathbb{R}^n$ is a bounded domain and $1<q<p<r<p^*$. It is well known that there exists a number $Lambda_{q,r}>0$ such that the problem admits at least two positive solutions for $0<Lambda<Lambda_{q,r}$, at least one positive solution for $Lambda=Lambda_{q,r}$, and no positive solution for $Lambda > Lambda_{q,r}$. We show that [ lim_{q to p} Lambda_{q,r} = lambda_1(p), ] where $lambda_1(p)$ is the first eigenvalue of the p-laplacian. It is worth noticing that $lambda_1(p)$ is the threshold for existence/nonexistence of positive solutions to the above problem in the limit case $q=p$." @default.
- W4299596004 created "2022-10-02" @default.
- W4299596004 creator A5039019828 @default.
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- W4299596004 date "2014-05-03" @default.
- W4299596004 modified "2023-09-26" @default.
- W4299596004 title "On the existence threshold for positive solutions of p-laplacian equations with a concave-convex nonlinearity" @default.
- W4299596004 hasPublicationYear "2014" @default.
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