Impulsive resonance periodic problems of first order. (English) Zbl 1022.34025

Nieto, J. J.

Appl. Math. Lett. 15, No. 4, 489-493 (2002).

A theorem on the existence of solutions to the nonlinear periodic boundary value problem \[ u'(t)+ F(t, u(t))= 0,\quad t\neq t_1,\dots, t_p,\quad u(t^+_j)= u(t^-_j)+ I_j(u(t^-_j)),\quad j= 1,\dots, p, \] is proved.

Reviewer: Stepan Kostadinov (Plovdiv)

MSC:

34B37	Boundary value problems with impulses for ordinary differential equations
34C25	Periodic solutions to ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

impulsive differential equation; periodic boundary value problem; Green’s function; sublinear nonlinearity; sublinear growth

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