Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains

Electronic Journal of Differential Equations

关键词: Critical indefinite nonlinearity;    bifurcation;    a priori estimates.;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $$ - Delta u =lambda u + h (x) u^{(n+2)/(n-2)} $$ ina smooth openbounded domain $Omegasubseteq mathbb{R}^n$,$n > 4 $ with Dirichlet boundary conditions and for $lambdageq 0 $. Under suitable assumptions on the weight function, we obtain the positive solution branch, bifurcating from the first eigenvalue $lambda_1(Omega)$. For $n=2$, we get similar results for $-Delta u =lambda u + h (x)phi(u)e^u$ where $phi$ is bounded and superlinear near zero.

【 授权许可】

Unknown