Superlinear indefinite elliptic problems and Pohozyaev type identities
In this paper one seeks nonzero solutions for the Dirichlet problem \(-\Delta u=\mu u+a(x)g(u),\) \(u\in H^1_0(\Omega)\), where \(\Omega\) is a bounded domain in \(\text{ I R}^N\), \(\mu>0\), \(a\in C^2(\overline\Omega)\) changes sign in \(\Omega\) and \(g\) is superlinear both at zero and at infinity. Under a hypothesis implying that the zero set \(\Omega^0=\{x\in\overline\Omega:a(x)=0\}\) has Lebesgue measure zero, the authors prove that the above problem has a nonzero solution.
scientific article; zbMATH DE number 1268058
scientific article