Positive solutions of nonlinear second-order periodic boundary value problems

Abstract

In this paper, we consider the nonlinear second-order periodic boundary value problemwhere the nonlinear term f is a Caratheodory function. By introducing two height functions concerned with f and considering the integrals of height functions on some bounded sets, we prove the existence and multiplicity of positive solutions for the problem.

Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

“…; N with the reproducing kernel function R x y ð Þ on 0; 1 ½ , the approximate solution u N n ðxÞ is calculated by Eq. (14). The numerical results at some selected grid points for N ¼ 101 and n ¼ 5 are given in Table 3.…”

“…In [13] the authors have discussed the existence of nontrivial periodic solutions for second-order periodic BVPs. In [14] also, the author has provided the existence and multiplicity of positive solutions to further investigation to second-order periodic BVPs. Furthermore, the existence of solutions is carried out in [15] for third-order periodic BVPs.…”

Existence of nontrivial periodic solutions for a nonlinear second order periodic boundary value problem

“…(1.2) Due to a wide range of applications in physics and engineering, second order periodic boundary value problems have been investigated by many authors [1][2][3][4][5][6][7][8][9][10]. When a(t) ≡ 0 and ω = 2π , in [11], Yao obtained the conditions for the existence of single positive solution and multiple positive solutions for the following PBVP…”

Periodic Positive Solution to a Class of Singular Second-Order Ordinary Differential Equations

“…Here, the function u * is called a positive solution of (P ) if u * is a solution of (P ) and u * (t) > 0, 0 ≤ t ≤ 2π . Recently, the fixed point theorems on a cone have been applied successfully to obtain the existence of positive solutions of (P ), for details, see [20][21][22][23][24] and references therein.…”