Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains
In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $$ - Delta u =lambda u + h (x) u^{(n+2)/(n-2)} $$ in a smooth open bounded domain $Omegasubseteq mathbb{R}^n$, $n > 4 $ with Dirichlet boundary conditions and for $lambd...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2007-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/15/g2/abstr.html |
| Summary: | In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $$ - Delta u =lambda u + h (x) u^{(n+2)/(n-2)} $$ in a smooth open bounded domain $Omegasubseteq mathbb{R}^n$, $n > 4 $ with Dirichlet boundary conditions and for $lambda geq 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. |
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| ISSN: | 1072-6691 |