Existence And Multiplicity To Solutions For Nonlinear Kirchhoff-Schrodinger-Poisson Systems

Nonlinear partial differential equations usually arise in the natural science and engi-neering areas. Since they have a broad application background and important research value in biology, chemistry, physics and other fields of science, a large number of researchers have devoted much attention to these equations for a long time. Moreover, for Kirchhoff equations and Schrodinger equations as the most fundamental equations in the partial differential equa-tions, the existence, multiplicity and nonexistence of solutions have also attracted extensive attention in recent years.In this paper, we use variational methods, such as the Symmetric mountain pass theo-rem, the Cut-off function and Pohozeav type identity, to discuss the existence and multiplicity of solutions for two special kinds of Kirchhoff-Schrodinger-Poisson systems.The thesis consists of three sections.Chapter 1 is the preface.In Chapter 2, we study the existence of solutions for the following Kirchhoff-Schrodinger-Possion system Using the Symmetric mountain pass theorem, we have the following theorem. Theorem 2.1.1 Assume that (V), (1), (f1)-(f3) hold, then the system above possessesinfinitely many nontrivial solutions{un,φun} withIn Chapter 3, we study the following Kirchhoff-Schrodinger-Possion systemwhere a, V are positive constants and b≥0, λ> 0 are parameter, g, f satisfy the following conditions:(g) g ∈ C(R+,R+) and there exists C> 0 such that |g(t)|≤ C{|t|+|t|p) for all t ∈ R+, where p ∈ (2,4);By the variational method of the combination of a cut-off function and a Pohozeav type identity, we obtain the following result.Theorem 3.1.1 Assume that (g), (f4)-(f6) hold, then there exist bo> 0, λ0> 0 such that for any b ∈ [0,b0), λ ∈ [0, λ0), the system above has at least one positive radical solution...