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Contents¡¶²©Ê¿ºóÎÄ¿â¡·ÐòÑÔPrefaceChapter 1 Schr.dinger-Poisson Equations 11.1 Schr.dinger-Poisson equations with sign-changing potential 11.1.1 Introduction and main results 11.1.2 Variational setting and compactness condition 41.1.3 Proofs of main results 151.2 Nonlinear Schr.dinger-Poisson equations with sublinear case 211.2.1 Introduction and main results 211.2.2 Variation set and proofs of main results 241.3 Nonlinear term involving a combination of concave and convex terms.271.3.1 Existence of solution.271.3.2 The multiplicity of solutions.311.3.3 The proof of Theorem 1.6 35Chapter 2 Klein-Gordon-Maxwell System 372.1 Two solutions for nonhomogeneous Klein-Gordon-Maxwell system 372.1.1 Introduction and main results 372.1.2 Variational setting and compactness condition 412.1.3 Proofs of main results 542.2 The primitive of the nonlinearity f is of 2-superlinear growth at infinity 612.2.1 Introduction and main results 612.2.2 Variational setting and compactness condition 642.2.3 Proofs of main results 702.3 Proofs of results 712.3.1 The proof of Theorem 2.5 742.3.2 The proof of Theorem 2.6 792.4 Ground state solutions for critical Klein-Gordon-Maxwell equations 852.4.1 Introduction and main results 852.4.2 Variational setting and preliminaries 862.4.3 The Nehari manifold N 892.4.4 Proofs of main results 92Chapter 3 Klein-Gordon Equation Coupled with Born-Infeld Theory 963.1 Introduction and main results.963.2 Variational setting and compactness condition 1003.3 Proofs of main results 106Chapter 4 Localized Nodal Solutions for Kirchhoff Equations 1084.1 Introduction and main results.1084.2 Variational setting and compactness condition 1134.3 Existence of multiple sign-changing critical points of ¦£" 1184.4 The proof of Theorem 4.1 1214.5 Proof of Proposition 4.2 134Chapter 5 Infinitely Many Sign-Changing Solutions 1385.1 Sign-changing solutions for an elliptic equation involving critical Sobolev and Hardy-Sobolev exponent 1385.1.1 Introduction and main results 1385.1.2 Preliminaries 1425.1.3 Auxiliary operator and invariant subsets of descending flow. 1445.1.4 The proof of Theorem 5.11465.2 Infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy-Sobolev-Maz'ya terms.1525.2.1 Introduction and main results 1525.2.2 Preliminaries 1565.2.3 Auxiliary operator and invariant subsets of descending flow. 1585.2.4 The proof of Theorem 5.3 1605.3 Sign-changing solutions for Hardy-Sobolev-Maz'ya equation involving critical growth 1665.3.1 Introduction and main results 1665.3.2 Preliminaries 1705.3.3 Auxiliary operator and invariant subsets of descending flow. 1735.3.4 The proof of Theorem 5.5 175Chapter 6 Multiple Solutions for Nonhomogeneous Choquard Equations 1826.1 Introduction and main results.1826.2 Variational setting and compactness condition 1856.3 Local minimum solution 1926.4 The proof of Theorem 6.2 202References 218Index 232±àºó¼Ç 233