论文标题
存在针对一类准线性schrödinger方程的阳性溶液，在非反射性Orlicz-Sobolev空间上，无穷大的潜在消失
Existence of positive solution for a class of quasilinear Schrödinger equations with potential vanishing at infinity on nonreflexive Orlicz-Sobolev spaces
论文作者
论文摘要
在本文中，我们研究了可能是非反射性的orlicz-sobolev空间上的一类准线性问题的阳性解决方案的存在 $$ - δ_φU +V（x）ϕ（| u |）u = k（x）f（u）\ mbox {in} \ mathbb {r} 其中$ n \ geq2 $，$ v，k $是非负连续功能，而$ f $是一种连续的功能，具有准智力增长。在这里，我们将在\ cite {alvesandmarco}中呈现的硬性型不平等扩展到非反射性的Orlicz空间。通过不平等，以及用于非差异功能的变异方法，我们将获得基态解决方案。我们还分析了$ v = 0 $的问题。
In this paper we investigate the existence of positive solution for a class of quasilinear problem on an Orlicz-Sobolev space that can be nonreflexive $$- Δ_Φ u +V(x)ϕ(|u|)u= K(x)f(u)\mbox{ in } \mathbb{R}^{N}$$ where $N\geq2$, $V,K$ are nonnegative continuous functions and $f$ is a continuous function with a quasicritical growth. Here we extend the Hardy-type inequalities presented in \cite{AlvesandMarco} to nonreflexive Orlicz spaces. Through inequalities together with a variational method for non-differentiable functionals we will obtain a ground state solution. We analyze also the problem with $V=0$.
