Periodic Boundary Value Problem for First Order Impulsive Differential Equation at Resonance
نویسندگان
چکیده
We develop a general theorem concerning the existence of solutions to the periodic boundary value problem for the first-order impulsive differential equation, x′(t) = f(t, x(t)), t ∈ J \ {t1, t2, · · · , tk} 4x(ti) = Ii(x(ti)), i = 1, 2 · · · k x(0) = x(T ). And using it we get a concrete existence result. Moreover, to our knowledge the coincidence degree method has not been used to the first order impulsive differential systems. Besides, our results can also be applied in studying the usual periodic boundary value problem at resonance without impulses.
منابع مشابه
Existence and uniqueness of solutions for a periodic boundary value problem
In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.
متن کاملSolvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance
Differential equation with fractional order have recently proved valuable tools in the modeling of many phenomena in various fields of science and engineering [1-5]. Recently, many researchers paid attention to existence result of solution of the boundary value problems for fractional differential equations at nonresonance, see for examples [6-15]. But, there are few papers which consider the b...
متن کاملAn analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients. At first, the non-self-adjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence ...
متن کاملPeriodic boundary value problems for nonlinear impulsive fractional differential equation
In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.
متن کاملOn Periodic Boundary Value Problems of First-order Perturbed Impulsive Differential Inclusions
In this paper we present an existence result for a first order impulsive differential inclusion with periodic boundary conditions and impulses at the fixed times under the convex condition of multi-functions.
متن کامل