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书名 | 几类非线性偏微分方程解的存在性和多重性(英文版)/博士后文库 |
分类 | 科学技术-自然科学-数学 |
作者 | 王丽霞 |
出版社 | 科学出版社 |
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简介 | 内容推荐 本书主要介绍了太阳磁场理论和观测的基本原理和进展。本书讨论了从太阳观测的测量设备到太阳磁场的演化、磁能的储存、太阳大气中的磁螺度及其与太阳周期的关系等课题。太阳磁学作为太阳物理和空间天气研究的重要组成部分,涵盖了太阳爆发过程中磁场的形成、发展和耗散。本书还介绍了太阳磁剪切、电流、磁螺度和太阳周期的测量与观测的新进展。 目录 《博士后文库》序言 Preface Chapter 1 Schr.dinger-Poisson Equations 1.1 Schr.dinger-Poisson equations with sign-changing potential 1.1.1 Introduction and main results 1.1.2 Variational setting and compactness condition 1.1.3 Proofs of main results 1.2 Nonlinear Schr.dinger-Poisson equations with sublinear case 1.2.1 Introduction and main results 1.2.2 Variation set and proofs of main results 1.3 Nonlinear term involving a combination of concave and convex terms 1.3.1 Existence of solution 1.3.2 The multiplicity of solutions 1.3.3 The proof of Theorem 1.6 Chapter 2 Klein-Gordon-Maxwell System 2.1 Two solutions for nonhomogeneous Klein-Gordon-Maxwell system 2.1.1 Introduction and main results 2.1.2 Variational setting and compactness condition 2.1.3 Proofs of main results 2.2 The primitive of the nonlinearity f is of 2-superlinear growth at infinity 2.2.1 Introduction and main results 2.2.2 Variational setting and compactness condition 2.2.3 Proofs of main results 2.3 Proofs of results 2.3.1 The proof of Theorem 2.5 2.3.2 The proof of Theorem 2.6 2.4 Ground state solutions for critical Klein-Gordon-Maxwell equations 2.4.1 Introduction and main results 2.4.2 Variational setting and preliminaries 2.4.3 The Nehari manifold N 2.4.4 Proofs of main results Chapter 3 Klein-Gordon Equation Coupled with Born-Infeld Theory 3.1 Introduction and main results 3.2 Variational setting and compactness condition 3.3 Proofs of main results Chapter 4 Localized Nodal Solutions for Kirchhoff Equations 4.1 Introduction and main results 4.2 Variational setting and compactness condition 4.3 Existence of multiple sign-changing critical points of Γ 4.4 The proof of Theorem 4.1 4.5 Proof of Proposition 4.2 Chapter 5 Infinitely Many Sign-Changing Solutions 5.1 Sign-changing solutions for an elliptic equation involving critical Sobolev and Hardy-Sobolev exponent 5.1.1 Introduction and main results 5.1.2 Preliminaries 5.1.3 Auxiliary operator and invariant subsets of descending flow 5.1.4 The proof of Theorem 5.1 5.2 Infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy-Sobolev-Maz'ya terms. 5.2.1 Introduction and main results 5.2.2 Preliminaries 5.2.3 Auxiliary operator and invariant subsets of descending flow 5.2.4 The proof of Theorem 5.3 5.3 Sign-changing solutions for Hardy-Sobolev-Maz'ya equation involving critical growth 5.3.1 Introduction and main results 5.3.2 Preliminaries 5.3.3 Auxiliary operator and invariant subsets of descending flow. 5.3.4 The proof of Theorem 5.5 Chapter 6 Multiple Solutions for Nonhomogeneous Choquard Equations 6.1 Introduction and main results 6.2 Variational setting and compactness condition 6.3 Local minimum solution 6.4 The proof of Theorem 6.2 References Index 编后记 |
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