Multiple Solutions for a Class of BVPs of Second-Order Discontinuous Differential Equations with Impulse Effects

Existence of Homoclinic Solutions for a Class of Second-Order Differential Equations with Multiple Lags

This paper is concerned with the existence of homoclinic orbits for secondorder differential equations with multiple lags. By using Mawhin’s continuation theorem, a nontrivial homoclinic orbit is obtained as a limit of a certain sequence of periodic solutions of the equation. AMS Subject Classifications: 34K15, 34C25.

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

Periodic solutions of second-order differential equations with multiple delays

* Correspondence: [email protected] School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, P. R. China Full list of author information is available at the end of the article Abstract By using the critical point theory and S index theory, we obtain a new result for the existence and multiplicity of periodic solutions for a class of second-order...

MULTIPLE NONNEGATIVE SOLUTIONS FOR BVPs OF FOURTH-ORDER DIFFERENCE EQUATIONS

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t− 2) = a(t) f (x(t)), t ∈ [2,T], x(0)= x(T +2)=0, Δ2x(0)=Δ2x(T)=0 are established by using the well-known LeggettWilliams fixed point theorem, and then, for arbitrary positive integerm, existence results for at least 2m− 1 nonnegative solutions are ...

Existence of Three Monotone Solutions of Nonhomogeneous Multipoint BVPs for Second-Order Differential Equations

Recommended by Jean Mawhin This paper is concerned with nonhomogeneous multipoint boundary value problems of second-order differential equations with one-dimensional p-Laplacian. Sufficient conditions to guarantee the existence of at least three solutions may be not positive of these BVPs are established.