Three critical points theorem and its application to quasilinear elliptic equations

Abstract

In this paper, we prove a Pucci-Serrin type three critical points theorem for continuous functionals and study its application to quasilinear elliptic equations with natural growth.

Multiplicity of Periodic Solutions for a Higher Order Difference Equation

“…In recent years, much attention has been given to second order Hamiltonian systems and elliptic boundary value problems by a number of authors; see [1][2][3] and references therein. On one hand, there have been many approaches to study periodic solutions of differential equations or difference equations, such as critical point theory (which includes the minimax theory, the Kaplan-Yorke method, and Morse theory), fixed point theory, and coincidence theory; see, for example, [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”