描述
开 本: 16开纸 张: 胶版纸包 装: 平装是否套装: 否国际标准书号ISBN: 9787030774545
内容简介
《几类非线性偏微分方程解的存在性和多重性(英文)》主要介绍了太阳磁场理论和观测的基本原理和进展。《几类非线性偏微分方程解的存在性和多重性(英文)》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。《几类非线性偏微分方程解的存在性和多重性(英文)》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
Contents
《博士后文库》序言
Preface
Chapter 1 Schr.dinger-Poisson Equations 1
1.1 Schr.dinger-Poisson equations with sign-changing potential 1
1.1.1 Introduction and main results 1
1.1.2 Variational setting and compactness condition 4
1.1.3 Proofs of main results 15
1.2 Nonlinear Schr.dinger-Poisson equations with sublinear case 21
1.2.1 Introduction and main results 21
1.2.2 Variation set and proofs of main results 24
1.3 Nonlinear term involving a combination of concave and convex terms.27
1.3.1 Existence of solution.27
1.3.2 The multiplicity of solutions.31
1.3.3 The proof of Theorem 1.6 35
Chapter 2 Klein-Gordon-Maxwell System 37
2.1 Two solutions for nonhomogeneous Klein-Gordon-Maxwell system 37
2.1.1 Introduction and main results 37
2.1.2 Variational setting and compactness condition 41
2.1.3 Proofs of main results 54
2.2 The primitive of the nonlinearity f is of 2-superlinear growth at infinity 61
2.2.1 Introduction and main results 61
2.2.2 Variational setting and compactness condition 64
2.2.3 Proofs of main results 70
2.3 Proofs of results 71
2.3.1 The proof of Theorem 2.5 74
2.3.2 The proof of Theorem 2.6 79
2.4 Ground state solutions for critical Klein-Gordon-Maxwell equations 85
2.4.1 Introduction and main results 85
2.4.2 Variational setting and preliminaries 86
2.4.3 The Nehari manifold N 89
2.4.4 Proofs of main results 92
Chapter 3 Klein-Gordon Equation Coupled with Born-Infeld Theory 96
3.1 Introduction and main results.96
3.2 Variational setting and compactness condition 100
3.3 Proofs of main results 106
Chapter 4 Localized Nodal Solutions for Kirchhoff Equations 108
4.1 Introduction and main results.108
4.2 Variational setting and compactness condition 113
4.3 Existence of multiple sign-changing critical points of Γ” 118
4.4 The proof of Theorem 4.1 121
4.5 Proof of Proposition 4.2 134
Chapter 5 Infinitely Many Sign-Changing Solutions 138
5.1 Sign-changing solutions for an elliptic equation involving critical Sobolev and Hardy-Sobolev exponent 138
5.1.1 Introduction and main results 138
5.1.2 Preliminaries 142
5.1.3 Auxiliary operator and invariant subsets of descending flow. 144
5.1.4 The proof of Theorem 5.1146
5.2 Infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy-Sobolev-Maz’ya terms.152
5.2.1 Introduction and main results 152
5.2.2 Preliminaries 156
5.2.3 Auxiliary operator and invariant subsets of descending flow. 158
5.2.4 The proof of Theorem 5.3 160
5.3 Sign-changing solutions for Hardy-Sobolev-Maz’ya equation involving critical growth 166
5.3.1 Introduction and main results 166
5.3.2 Preliminaries 170
5.3.3 Auxiliary operator and invariant subsets of descending flow. 173
5.3.4 The proof of Theorem 5.5 175
Chapter 6 Multiple Solutions for Nonhomogeneous Choquard Equations 182
6.1 Introduction and main results.182
6.2 Variational setting and compactness condition 185
6.3 Local minimum solution 192
6.4 The proof of Theorem 6.2 202
References 218
Index 232
编后记 233
《博士后文库》序言
Preface
Chapter 1 Schr.dinger-Poisson Equations 1
1.1 Schr.dinger-Poisson equations with sign-changing potential 1
1.1.1 Introduction and main results 1
1.1.2 Variational setting and compactness condition 4
1.1.3 Proofs of main results 15
1.2 Nonlinear Schr.dinger-Poisson equations with sublinear case 21
1.2.1 Introduction and main results 21
1.2.2 Variation set and proofs of main results 24
1.3 Nonlinear term involving a combination of concave and convex terms.27
1.3.1 Existence of solution.27
1.3.2 The multiplicity of solutions.31
1.3.3 The proof of Theorem 1.6 35
Chapter 2 Klein-Gordon-Maxwell System 37
2.1 Two solutions for nonhomogeneous Klein-Gordon-Maxwell system 37
2.1.1 Introduction and main results 37
2.1.2 Variational setting and compactness condition 41
2.1.3 Proofs of main results 54
2.2 The primitive of the nonlinearity f is of 2-superlinear growth at infinity 61
2.2.1 Introduction and main results 61
2.2.2 Variational setting and compactness condition 64
2.2.3 Proofs of main results 70
2.3 Proofs of results 71
2.3.1 The proof of Theorem 2.5 74
2.3.2 The proof of Theorem 2.6 79
2.4 Ground state solutions for critical Klein-Gordon-Maxwell equations 85
2.4.1 Introduction and main results 85
2.4.2 Variational setting and preliminaries 86
2.4.3 The Nehari manifold N 89
2.4.4 Proofs of main results 92
Chapter 3 Klein-Gordon Equation Coupled with Born-Infeld Theory 96
3.1 Introduction and main results.96
3.2 Variational setting and compactness condition 100
3.3 Proofs of main results 106
Chapter 4 Localized Nodal Solutions for Kirchhoff Equations 108
4.1 Introduction and main results.108
4.2 Variational setting and compactness condition 113
4.3 Existence of multiple sign-changing critical points of Γ” 118
4.4 The proof of Theorem 4.1 121
4.5 Proof of Proposition 4.2 134
Chapter 5 Infinitely Many Sign-Changing Solutions 138
5.1 Sign-changing solutions for an elliptic equation involving critical Sobolev and Hardy-Sobolev exponent 138
5.1.1 Introduction and main results 138
5.1.2 Preliminaries 142
5.1.3 Auxiliary operator and invariant subsets of descending flow. 144
5.1.4 The proof of Theorem 5.1146
5.2 Infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy-Sobolev-Maz’ya terms.152
5.2.1 Introduction and main results 152
5.2.2 Preliminaries 156
5.2.3 Auxiliary operator and invariant subsets of descending flow. 158
5.2.4 The proof of Theorem 5.3 160
5.3 Sign-changing solutions for Hardy-Sobolev-Maz’ya equation involving critical growth 166
5.3.1 Introduction and main results 166
5.3.2 Preliminaries 170
5.3.3 Auxiliary operator and invariant subsets of descending flow. 173
5.3.4 The proof of Theorem 5.5 175
Chapter 6 Multiple Solutions for Nonhomogeneous Choquard Equations 182
6.1 Introduction and main results.182
6.2 Variational setting and compactness condition 185
6.3 Local minimum solution 192
6.4 The proof of Theorem 6.2 202
References 218
Index 232
编后记 233
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