Existence of nontrivial periodic solutions for first order functional differential equations

In this paper, in the case of not requiring the nonlinear terms to be non-negative the existence of nontrivial periodic solutions for the first order functional differential equations is considered by using the partial ordering theory.     

Anti-periodic solutions of nonlinear first order impulsive functional differential equations

The existence of anti-periodic solutions of the following nonlinear impulsive functional differential equations $$ x'(t) + a(t)x(t) = f(t,x(t),x(\alpha _1 (t)), \ldots ,x(\alpha _n (t))),t \in \mathbb{R},\Delta x(t_k ) = I_k (x(t_k )),k \in \mathbb{Z} $$ is studied. Sufficient conditions for the existence of at least one anti-periodic solution of the mentioned equation are established. Several new existence results are obtained.     

Stability results for the solutions of some third and fourth order differential equations

Summary The paper investigates conditions under which solutions of the equations (1) and (2) of § 1.1 tend to zero as t → ∞.     

Some existence results for differential equations of second order

Existence results for initial value problem and Dirichlet boundary value problem for nonlinear differential equations of second order are obtained.     

Extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order

This paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order, obtains the sufficient conditions for the existence of solutions by establishing a new comparison principle and using the monotone iterative technique. A concrete example is presented and solved to illustrate the obtained results.     

Global existence results for impulsive functional differential equations

In this paper, we investigate the existence of solutions of impulsive delay differential equation

     

On the existence of almost periodic solutions of some dissipative second order differential equations

Summary The search for almost periodic solutions of any dissipative equation of the form(1.1), in which p(t) is an almost periodic function, has come to be closely linked up with a number of standard ? convergence ? restrictions on f, g′, g″ and k (see, for example,[2] and[3]). The object of the present paper is to show that as far as the existence, alone, of an almost periodic solution of(1.1) is concerned these ? convergence ? restrictions on f, g′, g″ and k are quite unnecessary. The first result (Theorem 1) shows in fact that the conditions(1.2) alone are quite sufficient for the existence of an almost periodic solution of(1.1); and Theorem 2 extends this result (though under stronger conditions on f and g) to the case in which the forcing function depends on x and x as well. Partially supported by N.S.F. research project G-57 at The University of Michigan.     

Existence of periodic solutions for first order differential equations

In this paper we study the periodic boundary value problem for first order differential equations by combining techniques of the theory of differential inequalities, namely the method of upper and lower solutions, and the alternative method for nonlinear problems at resonance. The results obtained are in terms of the behavior of the nonlinear part at infinity.     

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

Let E be a finite-dimensional Banach space, let C⁰(R; E) be a Banach space of functions continuous and bounded on R and taking values in E; let K:C ⁰(R ,E) → C ⁰(R, E) be a c-continuous bounded mapping, let A: E → E be a linear continuous mapping, and let h ∈ C ⁰(R, E). We establish conditions for the existence of bounded solutions of the nonlinear equation

Existence theory for first order discontinuous functional differential equations

We prove the existence of extremal solutions for a first order functional differential equation subject to nonlinear boundary conditions of functional type. Moreover, the functions that define our problem are allowed to be discontinuous. The proof of our main result is based on a generalized iterative technique.

     

Asymptotically almost periodic solutions of abstract retarded functional differential equations of first order

We establish the existence of asymptotically almost periodic mild solutions for a class of semi-linear first-order abstract retarded functional differential equations with infinite delay.     

Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations

This paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations

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