The Study Of The Sign-changing Solutions For Two Kinds Of Kirchhoff Type Equations

In this paper,we mainly study the sign-changing solutions for two kinds of p-Laplacian Kirchhoff type equations.This article is mainly divided into two parts.The first part mainly introduces a class of Kirchhoff type equations under some suitableassumptions for the nonlinear term,we use the quantitative deformation lemma,degree theory,Non-Nehari manifold method and the counter example method to obtain the main results.The second part mainly studies the sign-changing solutions of the Kirchhoff type equation with a(2p-1)-linear growth nonlinearity.Remarkably,we use a new method to verify M_b?(?).Also,the second part can be regarded as a complementary work of the first part.The main results obtained in this paper are the existence of the sign-changing solution;the energy doubling property of the sign-changing solution,that is,the energy of the sign-changing solution is strictly larger than twice that of the ground state solution;the convergence property of the sign-changing solution as the parameter tends to zero.The details are arranged as follows.The first chapter mainly introduces the historical background and significance of the Kirchhoff type problem,the research status at home and abroad,and the main contents of this paper.The second chapter introduces the first problem of the paper,that is,the existence of the sign-changing solution for a class of p-Laplacian Kirchhoff type equations under some suitable assumptions and its corresponding properties of the sign-changing solution.In the third chapter,the second problem that the sign-changing solution of a class of p-Laplacian Kirchhoff type equations with a(2p-1)-linear growth nonlinearity is given.The main results are the existence of the sign-changing solution,the energy doubling property and the convergence property of the sign-changing solution.