Existence Theorem for a Class of Nonlinear Fourth-order Schrödinger-Kirchhoff-Type Equations.
Year: 2017
Author: Shiqiang Tang, Peng Chen, Xiaochun Liu
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 146–164
Abstract
This paper is concerned with the existence of nontrivial solutions for the following fourth-order equations of Kirchhoff type
{Δ2u−(a+b∫RN|∇u|2dx)Δu+λV(x)u=f(x,u),x∈RN,u∈H2(RN),
where a,b are positive constants, λ≥1 is a parameter, and the nonlinearity f is either superlinear or sublinear at infinity in u. With the help of the variational methods, we obtain the existence and multiplicity results in the working spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v30.n2.3
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 146–164
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Fourth-order elliptic equations
Author Details
Shiqiang Tang Email
Peng Chen Email
Xiaochun Liu Email