Existence of nontrivial solutions for a semilinear elliptic problem with supercritical exponent. (English) Zbl 1140.35443
Summary: Let \(N{\leqslant}3\), \(p>2^*=2N/(N-2)\) and \({\Omega}\subset{\mathbb R}^N\) be a bounded domain with a boundary \({\partial}\Omega\). Our purpose is to consider the existence of solutions of problem: \(-{\Delta}u=u^{p-1}\) on \({\Omega}\), \(u>0\) on \({\Omega}\), \(u=0\) on \({\partial}\Omega\).
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35B33 | Critical exponents in context of PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
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