On some polyharmonic elliptic equation with discontinuous and increasing nonlinearities (Q1680769)

The paper studies the problem \((-\Delta )^m u=f(x,u)+\lambda h(x)\) in \(\mathbb R^N\), where \(N\geq 5\). Here \(m\in N\), \(2\leq m<N/2\), \(\lambda >0\), \(h\in L^{2N/(N+2m)}(\mathbb R^N)\), \(h\neq 0\). Under some assumption on \(f\) it is shown that there exists \(\lambda_* >0\) such that for \(0<\lambda <\lambda_*\) the problem admits at least one nontrivial solution.