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As science and technology and the continuous development of the theory of mathematical foundations, a variety of nonlinear problems increasingly attracted widespread attention, nonlinear functional analysis has become an important research in modern mathematics directions. Because it can be a good explain various phenomena in nature and subject to domestic mathematics and natural sciences attention in recent years on nonlinear functional analysis studies to get some new results. awareness of mathematical physics and mathematical biology and other fields of research has also made considerable progress, nonlinear Schrodinger equation derived from mathematical physics, mathematical biology, physics and other disciplines, is the study of differential equations of one of the more active areas, and such equations and variable number of positive and negative solutions of Existence problem is a hot topic in recent years, this paper, using the invariant set down stream, the critical point theory, the minimax methods, a class of super-linear Schrodinger equation (Pλ) and variable number of positive and negative solutions of Existence issues paper is divided into three chapters: the first chapter, discussing (Pλ) the existence of changing solutions, we weaken the f (χ, u) consecutive terms, the study's equation is more general. Application invariant set of methods and critical point symmetry principle, α and f some assumptions, when λ gt; 0 sufficiently large, we get (Pλ) radially unbounded sequence of changing solution when N = 4 or N ≥ 6, λ gt; 0, the application of fountain critical point theorem and symmetry principle we get (Pλ) unbounded sequence of non-radial changing solution in the second chapter, α and f satisfy the conditions similar to the first chapter, But we construct different cones to discuss (Pλ) changing solution existence problem. Application invariant set method and critical point theory, we obtain (Pλ) Unbounded changing solution sequence if (?) χ ∈ RN , (?) nondecreasing on R, we discussed changing solutions uκ the number of nodes in the domain, changing solution uκ get at most κ 1 domain nodes in the third chapter, we discussed ( Pλ) Existence positive and negative issues. Application invariant set of methods and critical point theory, combined with the corresponding operator eigenvalue problem when λ is sufficiently large, we get the equation (Pλ) is a positive solution and a negative solution. innovation of this paper are: the general super-linear Schrodinger equation of the RN solution and the change in the number of positive and negative Existence articles compared to our weakened f (χ, u) consecutive terms, the equation of a more general study sex.
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