Multiplicity of Solutions for Fourth-Order Elliptic Equations with p-Laplacian and Mixed Nonlinearity

摘要

In the paper, we study the multiplicity of solutions for a class of fourth-order elliptic equations with p-Laplacian and mixed nonlinearity of the form: Delta 2u-Delta pu+lambda V(x)u=f(x,u)+mu xi(x)|u|q-2u,x is an element of RN,u is an element of H2(RN).<^>2u-Delta _{p}u+lambda V(x)u=f(x,u)+mu xi (x)ert uert <^>{q-2}u, xin {mathbb {R}}<^>N, uin H<^>{2}({mathbb {R}}<^>N). end{array} ight. end{aligned}$$end{document}Unlike most other works, we replace the Laplacian with a p-Laplacian. Using the mountain pass theorem and Ekeland's variational principle, we establish the existence of two nontrivial solutions. To overcome the difficulty of the convergence of the subsequences for the Palais-Smale sequences of the Euler-Lagrange functional, we consider Cerami sequences. Our results extend the recent results of Zhang et al. (Electron J Differ Equ 2017(250):1-15, 2017).