Bound state for fractional Schrödinger equation with saturable nonlinearity

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• 作者：Youyan Wan^a ; Zhengping Wang ; ^b ; ^{wangzp@wipm.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fractional Schrö ; dinger equation ; Bound state ; Ground state ; Mountain Pass Theorem
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：273
• 期：Complete
• 页码：735-740
• 全文大小：261 K

文摘

In this paper, we study the existence of bound state for the following fractional Schrödinger equationwhere α(−Δ)${(-\Delta )}^{\alpha }$ with α ∈ (0, 1) is the fractional Laplace operator defined as a pseudo-differential operator with the symbol |ξ|^2α, V(x) is a positive potential function and the nonlinearity f   is saturable, that is, f(u)/u→l∈(0,+∞)$f\left(u\right)/u\to l\in (0,+\infty )$ as |u|→+∞$\left|u\right|\to +\infty$. By using a variant version of Mountain Pass Theorem, we prove that there exists a bound state and ground state of (P) when V and f satisfy suitable assumptions.