Nonexistence of nontrivial solutions for a class of boundary value problems (Q2388042)

From the text: We consider the Dirichlet problem \[ \Delta u+g(x,\nabla u)+f(u)=0\text{ in } \Omega\subset\mathbb{R}^n, \] \[ u(x)|_{\partial \Omega}=0. \] We obtain conditions ensuring the existence of only trivial solutions, and also conditions ensuring the nonexistence of solutions.