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

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

“…To mention a few, the existence and multiplicity of positive solutions have been discussed to first-order periodic BVPs as described in [12]. 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.…”

Developing CRS iterative methods for periodic Sylvester matrix equation

“…Numerical results validate that the proposed methods are superior to some existing methods and that equivalent mathematical methods can show different numerical performance.where the coefficient matrices A j , B j , C j , D j , E j ∈ R m×m and the solutions X j ∈ R m×m are periodic with period λ, that is, A j+λ = A j , B j+λ = B j , C j+λ = C j , D j+λ = D j , E j+λ = E j , and X j+λ = X j . The periodic Sylvester matrix equation (1.1) attracts considerable attention because it comes from a variety of fields of control theory and applied mathematics [1][2][3][4][5][6][7][8][9][10][11][12].In recent years, many efficient iterative methods have been proposed to solve the periodic Sylvester matrix equation (1.1). For example, Hajarian [13,14] developed the conjugate gradient squared (CGS), biconjugate gradient stabilized (BiCGSTAB) and biconjugate residual methods for solving the periodic Sylvester matrix equation (1.1).…”

General Periodic Boundary Value Problem for Systems

“…If I      identity, then (1,1) reduces to the usual periodic boundary value problem for which the literature in both the scalar and systems versions is very extensive (We refer to [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and references therein). For instance a recent paper, Wang [4] obtained the existence of periodic solution of a class of non-autonomous second-order systems .…”

“…Even in the scalar case the existence of periodic solutions for problems with nonsingular and singular case has commanded much attention in recent years (see [13][14][15][16][17][18][19][20][21][22] and references therein. In particular, in [13][14][15] fixed point theorems in conical shells are used to obtain existence and multiplicity results, some of these are improved in this paper.…”

“…In this notes, we prove result in the case where f has no singularity. In scalar case problem see [16][17][18][19][20][21][22] and references therein.…”