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arXiv · 1312.4168

A priori estimates for nonlinear fourth order Schr\"odinger type equations

G. M. Cárdenas
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Abstract

We study the fourth order Schr\"odinger type differential inequality $-\Delta^2 u + \lambda V(x)u \geq a(x)u^q$ with $a,V\in L^1_{loc}(\mathbf{R}^N)$, both nonnegative, and $\lambda>0$. 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.

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G. M. Cárdenas. 2013-12-15. A priori estimates for nonlinear fourth order Schr\"odinger type equations. https://arxiv.org/abs/1312.4168

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