Existence and uniqueness of periodic solutions of second-order nonlinear differential equations

Abstract

This paper is concerned with the following second-order nonlinear differential equation: x(t)) = e(t).By applying Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence and uniqueness of periodic solutions for the above equation. Some recent results are known as the special cases of ours.

Regions of existence for a class of nonlinear diffusion type problems

“…If we assume g(x, s) = e (nx) , p(x) = x m , F (x, s) = e (nx) f (x, s), and B(s(0), s(1), s ′ (0)) = − a2 a1 s ′ (1) + C a1 , then (3)-( 4) is transformed into the NDBVP (1)- (2). Several researchers [1,2,9,10,[14][15][16]22,28,29] studied similar and other kind of generalized forms of differential equation (1) subject to suitable boundary conditions.…”

“…This paper is categorized into following sections. In Section 2, we construct Green's functions, with the help of Generalized Laguerre polynomial and the hypergeometric function and established Maximum Principle for nonhomogeneous linear BVP ( 15)- (16). In Section 3, with the support of coupled technique (monotone constructive technique with upper and lower solutions), the regions of existence are established for NDBVP.…”

New Qualitative Results for Solutions of Functional Differential Equations of Second Order

“…The approach in [16] is based on global bifurcation theorem. Jia and Shao [17] established sufficient conditions for the existence and uniqueness of periodic solutions of an ordinary differential equation of second order by applying Mawhin's continuation theorem of coincidence degree theory.…”