Existence of solitary wave solutions for the nonlinear Klein-Gordon equation coupled with Born-Infeld theory with critical Sobolev exponent

DOI10.1016/j.na.2011.04.002zbMath1219.35041OpenAlexW1973025578MaRDI QIDQ544188

Kejing Zhang, Kai-Min Teng

Publication date: 14 June 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.04.002

zbMATH Keywords

variational methods

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Set-valued operators (47H04) Initial value problems for second-order hyperbolic equations (35L15) Soliton solutions (35C08) Second-order semilinear hyperbolic equations (35L71)

Related Items (11)

The existence of multiple solutions for the Klein-Gordon equation with concave and convex nonlinearities coupled with Born-Infeld theory on \(\mathbf{R}^3\) ⋮ On the solitary solutions for the nonlinear Klein-Gordon equation coupled with Born-Infeld theory ⋮ Existence and multiplicity of sign-changing solutions for Klein-Gordon equation coupled with Born-Infeld theory with subcritical exponent ⋮ Infinitely many solutions for the Klein-Gordon equation with sublinear nonlinearity coupled with Born-Infeld theory ⋮ Existence of solutions for critical Klein-Gordon equations coupled with Born-Infeld theory in higher dimensions ⋮ Nontrivial solution for Klein-Gordon equation coupled with Born-Infeld theory with critical growth ⋮ Unnamed Item ⋮ Multiple solutions for nonhomogeneous Klein-Gordon-Maxwell equations on \(\mathbb{R}^3\) ⋮ Unnamed Item ⋮ Infinitely many solutions and least energy solutions for Klein–Gordon equation coupled with Born–Infeld theory ⋮ Ground state solution for the nonlinear Klein-Gordon equation coupled with Born-Infeld theory with critical exponents

Cites Work

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• Existence results for the Klein-Gordon-Maxwell equations in higher dimensions with critical exponents
• Solitary waves for nonlinear Klein-Gordon equations coupled with Born-Infeld theory
• Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations
• Best constant in Sobolev inequality
• Existence of solitary waves in higher dimensions
• Existence and non-existence of solitary waves for the critical Klein-Gordon equation coupled with Maxwell's equations
• Minimax theorems
• Solitary waves for Klein-Gordon-Maxwell system with external Coulomb potential
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Solitary Waves in Abelian Gauge Theories
• SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS
• Coupled Klein—Gordon and Born—Infeld-type equations: looking for solitary waves
• Foundations of the new field theory
• Born–Infeld type equations for electrostatic fields

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