On Existence and Multiplicity of Solutions for Some Nonlinea

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原出版社:科學
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書名:On Existence and Multiplicity of Solutions for Some Nonlinea
ISBN:9787030774545
出版社:科學
著編譯者:王麗霞
頁數:231
所在地:中國大陸 *此為代購商品
書號:1625880
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【台灣高等教育出版社簡體書】 On Existence and Multiplicity of Solutions for Some Nonlinea 787030774545 王麗霞

內容簡介

本書介紹了:Schr dinger-Poisson方程、Klein-Gordon-Maxwell系統、Klein-Gordon方程和Born-Infeld的理論耦合等內容,讓專業學生研究了解方程的存在性、解的多重性和這些方程的符號變化解。

目錄

《博士後文庫》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
編後記

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