PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

DOI10.1017/S0004972710001607zbMath1364.34056MaRDI QIDQ3065422

Jifeng Chu, Ziheng Zhang

Publication date: 5 January 2011

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Schauder's fixed point theoremperiodic solutionsign-changing potentialsingular differential equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Applications of operator theory to differential and integral equations (47N20) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Nonautonomous smooth dynamical systems (37C60)

Related Items (11)

Multiplicity of positive periodic solutions of Rayleigh equations with singularities ⋮ IMPULSIVE PERIODIC SOLUTIONS FOR SINGULAR PROBLEMS VIA VARIATIONAL METHODS ⋮ Existence for singular periodic problems: a survey of recent results ⋮ Existence of anti-periodic solutions for second-order ordinary differential equations involving the Fučík spectrum ⋮ Positive periodic wave solutions of singular non-Newtonian filtration equations ⋮ Fixed point theorems and periodic problems for nonlinear Hill's equation ⋮ Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities ⋮ An order-type existence theorem and applications to periodic problems ⋮ Positive periodic solution to an indefinite singular equation ⋮ Periodic solutions for second order singular damped differential equations ⋮ Existence and multiplicity of solutions for a periodic Hill's equation with parametric dependence and singularities

Cites Work

• Infinitely many \(T\)-periodic solutions for a problem arising in nonlinear elasticity
• Weak singularities may help periodic solutions to exist
• Collisionless orbits of singular and non singular dynamical systems
• Positive periodic solutions of Hill's equations with singular nonlinear perturbations
• Rotation numbers and Lyapunov stability of elliptic periodic solutions
• Recent existence results for second-order singular periodic differential equations
• Upper and lower solutions for a generalized Emden-Fowler equation
• Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces
• Forced singular oscillators and the method of lower and upper solutions
• Multiplicity of positive periodic solutions to superlinear repulsive singular equations
• Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem
• Non-collision periodic solutions of forced dynamical systems with weak singularities
• On the sign of the Green's function associated to Hill's equation with an indefinite potential
• Periodic solutions of second order non-autonomous singular dynamical systems
• Subharmonic Solutions for Some Second-Order Differential Equations with Singularities
• Applications of Schauder's fixed point theorem to singular differential equations
• A relationship between the periodic and the Dirichlet BVPs of singular differential equations
• Higher order non‐resonance for differential equations with singularities
• A Lyapunov-type stability criterion using $L^\alpha $ norms
• A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle
• Periodic solutions of singular systems without the strong force condition
• Impulsive periodic solutions of first-order singular differential equations
• Multiplicity of positive periodic solutions to second order differential equations
• Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity
• Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems

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