Nonlocal Kirchhoff Superlinear Equations with Indefinite Nonlinearity and Lack of Compactness

作者：Li, Lin; Radulescu, Vicentiu^*; Repovs, Dusan

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2016, 17(6): 325-332.

DOI：10.1515/ijnsns-2016-0006

• mountain pass
• Ekeland variational principle
• nonlocal Kirchhoff equation

We study the following Kirchhoff equation:
- (1 + b integral(R3) vertical bar Delta u vertical bar(2)dx)Delta u + V(x)u = f(x, u), x is an element of R-3.
A feature of this paper is that the nonlinearity f and the potential V are indefinite, hence sign-changing. Under some appropriate assumptions on V and f, we prove the existence of two different solutions of the equation via the Ekeland variational principle and the mountain pass theorem.

• 出版日期2016-9
• 单位重庆工商大学