Study On The Existence Of Solutions Of Kirchhoff Type Equations On Time Scales

Based on the critical point theory,this paper is concerned with the existence of the weak solution of Kirchhoff type equation in two-point boundary value problem on time scale.The full text is divided into four chapters:In the first chapter,the backgrounds of the problem and the main work of this paper are introduced.In the second chapter,the preliminary knowledge of this article is introduced.In chapter 3,the existence of the weak solution of the nonlinear term f(?(t),x(?(t)))of the following equation(?)(2)under the superlinear condition is investigated.where T is the time scale,a is the forward jump operator.We use the mountain pass lemma to prove that there is at least one nontrivial weak solution to the above boundary value problem.In chapter 4,we mainly discuss the existence of the weak solution of the non-linear term f(?(t),x(?(t)))for problem(2)under asymptotically linear conditions.We use the critical point theory and the related properties of the first eigenvalue to obtain that there is at least one nontrivial weak solution to the above problem.