A priori estimates for nonlinear fourth order Schrödinger type equations
We study the fourth order Schrödinger type differential inequality $-Δ^2 u + λV(x)u \geq a(x)u^q$ with $a,V\in L^1_{loc}(\mathbf{R}^N)$, both nonnegative, and $λ>0$. We consider nonnegative solutions without making any assumptions about their asymptotic behavior, and choosing appropriate test functions, we find a priori estimates for some type of subharmonic solutions. Finally, applying these a priori estimates, we proof a Liouville type result.
math.AP↗