The existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method

DOI10.1016/j.na.2010.03.035zbMath1198.34037OpenAlexW2088950727WikidataQ115343050 ScholiaQ115343050MaRDI QIDQ975843

Juntao Sun, Liu Yang, Haibo Chen

Publication date: 11 June 2010

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.2010.03.035

zbMATH Keywords

local linkingboundary value problemscritical pointsvariational methodimpulsive differential equations

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Parameter dependent boundary value problems for ordinary differential equations (34B08) Boundary value problems with impulses for ordinary differential equations (34B37)

Related Items (42)

Existence results for \(\phi\)-Laplacian impulsive differential equations with periodic conditions ⋮ Existence and multiplicity of solutions for some damped Dirichlet nonlinear impulsive differential equations ⋮ Morse theory and local linking for a class of boundary value problems with impulsive effects ⋮ Multiplicity of solutions for impulsive differential equation on the half-line via variational methods ⋮ Eigenvalue problem of an impulsive differential equation governed by the one-dimensional p-Laplacian operator ⋮ Infinitely many solutions for nonlinear periodic boundary value problem with impulses ⋮ An application of variational method to second-order impulsive differential equation on the half-line ⋮ Existence of nontrivial weak homoclinic orbits for second-order impulsive differential equations ⋮ Existence and multiplicity of solutions for second-order impulsive differential equations with Dirichlet problems ⋮ New existence and multiplicity of solutions for some Dirichlet problems with impulsive effects ⋮ Analysis of a class of nonlinear fractional differential models generated by impulsive effects ⋮ The existence and multiplicity of solutions for second-order impulsive differential equations on the half-line ⋮ Bifurcation type phenomena for positive solutions of a class of impulsive differential equations ⋮ The existence of one solution for impulsive differential equations via variational methods ⋮ Infinitely many solutions for a class of nonlinear impulsive differential equations with periodic boundary conditions ⋮ Existence of subharmonic solutions for a class of second-order \(p\)-Laplacian systems with impulsive effects ⋮ Subharmonic solutions with prescribed minimal periodic for a class of second-order impulsive functional differential equations ⋮ Infinitely many solutions for second-order Hamiltonian system with impulsive effects ⋮ Periodic solutions for second order Hamiltonian systems with impulses via the local linking theorem ⋮ Positive solutions for a second-order \(p\)-Laplacian boundary value problem with impulsive effects and two parameters ⋮ The solutions of Sturm-Liouville boundary-value problem for fourth-order impulsive differential equation via variational methods ⋮ Existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects ⋮ Parameter dependence of positive solutions for second-order singular Neumann boundary value problems with impulsive effects ⋮ Multiple solutions to damped Hamiltonian systems with impulsive effects ⋮ Positive solutions for classes of multi-parameter fourth-order impulsive differential equations with one-dimensional singular \(p\)-Laplacian ⋮ Existence of homoclinic solutions for a class of second order \(p\)-Laplacian systems with impulsive effects ⋮ Periodic solution of second-order impulsive delay differential system via generalized mountain pass theorem ⋮ Periodic solution generated by impulses for singular differential equations ⋮ Existence of solutions for a class of second-order \(p\)-Laplacian systems with impulsive effects. ⋮ Infinitely many periodic solutions to a class of perturbed second-order impulsive Hamiltonian systems ⋮ Existence of infinitely many solutions for fourth-order impulsive differential equations ⋮ Infinitely many solutions for a boundary value problem with impulsive effects ⋮ Existence of solutions for a damped nonlinear impulsive problem with Dirichlet boundary conditions ⋮ Triple positive solutions of fourth-order impulsive differential equations with integral boundary conditions ⋮ Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems ⋮ MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATION VIA VARIATIONAL METHODS ⋮ Infinitely many solutions for a p-Laplacian boundary value problem with impulsive effects ⋮ Variational approach to a singular second-order systems with impulses effects ⋮ Infinitely many rotating periodic solutions for local superquadratic damped Hamiltonian systems with sublinear impulsive effects ⋮ Variational approach to some damped Dirichlet problems with impulses ⋮ Periodic solution of second order impulsive delay differential systems via variational method ⋮ Applications of variational methods to Sturm-Liouville boundary-value problem for fourth-order impulsive differential equations

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