Existence and multiplicity of positive solutions for fractional Schrödinger equations with critical growth

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• 作者：Fei Tao ; Xian Wu ; ^{wuxian2042@163.com}
• 关键词：Fractional Schrö ; dinger equations ; Ground state solutions ; Variational methods
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：158-174
• 全文大小：705 K
• 卷排序：35

文摘

In this paper, we study the existence and multiplicity of positive solutions for the fractional Schrödinger equations ε2α(−Δ)αu+V(x)u=∣u∣2α∗−2u+σg(x,u),x∈RN, where εε and σσ are positive parameters, 0<α<10<α<1, (−Δ)α denotes the fractional Laplacian of order αα, N>2αN>2α and 2α∗=2NN−2α is the fractional critical exponent, V∈C(RN,R+)V∈C(RN,R+), g∈C(RN×R,R)g∈C(RN×R,R). By the variational methods we study the existence and multiplicity of positive solutions. Our main results improve corresponding results in Shang and Zhang (2014).