Variational Approach To Anti-periodic Solutions For Several Kinds Of P-Laplacian Differential Equations

In this dissertation,we constructed the corresponding variational structure of the p-Laplacian differential equation with damping term,the p-Laplacian differential equation with the impulsive effects and the another p-Laplacian impulsive differential equation with damping term on the appropriate Sobolev spaces.We can reduce the problem of finding antiperiodic solutions for these differential equtions to that of seeking the critical points of the corresponding functional.Then,based on the different characteristics of nonlinear terms in differential equations,we present some sufficient conditions for the existence and multiplicity of antiperiodic solutions for these three kinds of p-Laplacian differential equations by using the minimax action principle,mountain pass lemma and fountain theorem.The results obtained by these methods extend some of the existing research results and extend the application range of the variational method in the the study of antiperiodic solution of the p-Laplacian differential equation.