The Existence Of Solutions For High Power Ultra-short Laser Channel Model Equation

In this paper,we discuss the existence of solutions for a class of quasilinear Schr¨odinger equations by using the Mountain Pass Lemma,Palais-Smale conditions and the Fountain Theorem.The paper is divided into four chapters.In the first chapter,we mainly introduce research background and research status of the article.What's more,we also simply introduce the research content of the article.In the second chapter,we give some definitions,theorems and important inequalities,which are associated with the article.In the third chapter,we study the existence of standing waves for the following periodic Schr¨odinger equation by using the variational method,the Fountain Theorem and the Fountain Duality Theorem.In the fourth chapter,we study the existence of ground state for the following periodic Schr¨odinger equation under the circumstance that the nonlinear term satisfies odd conditions by using the Mountain Pass Lemma and variationalmethod.