Periodic boundary value problem.
Mar 1, 2009 · Motivated by Liu [Y.
Periodic boundary value problem Introduction Consider the periodic boundary-value problem u00= p(t)u+ q(t); u(0) = u(!); u0(0) = u0(!); (1. 3 Chen & Xue: PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM 575 v(x,0) = f(x), vt(x,0) = ?(x), xGR. We first introduce definitions of principal part and order at $\pm\infty i$ for periodic analytic functions through detailed analysis. Jiang, X. We give a new definition of exponential notations and impulsive integrals for constructing the Green function and a comparison result of the linear problems with impulses. Finally Oct 24, 2012 · This paper is concerned with the existence of extremal solutions of periodic boundary value problems for second-order impulsive integro-differential equations with integral jump conditions. Aug 6, 2020 · Abstract We study periodic boundary value problems for a second-order linear partial differential equation with constant coefficients in a half-plane under various assumptions about the roots of the characteristic equation. Next Key Concepts: Eigenvalue Problems, Sturm-Liouville Boundary Value Problems; Robin Boundary conditions. Li, X. [X. 1 and 11. Appl. Dec 17, 2024 · We prove the uniqueness of fixed point (FP) and common fixed point (CFP) theorems under the new product types of rational contractions in generalized metric spaces with the application of boundary value problem. Solution:Again, we consider three cases. Math. We establish conditions for the unique solvability of periodic bound-ary value problem for second-order linear equations. Published: 09 March 2018 Volume 22, pages 1269–1279, (2018) Nov 15, 2010 · The existence of minimal and maximal solutions and the uniqueness of the solution for the periodic boundary value problem (1. (1. 9) First of all, we shall prove that the periodic boundary value problem of the auxiliary equation (1. Mar 9, 2018 · Existence of positive solutions for periodic boundary value problem with sign-changing Green’s function. case 1: If λ = 0, then the equation is φ′′ = 0 with general solution φ(x) = Ax + B. Liu, Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations, J. Dec 1, 2002 · The paper is organized as follows. (1c) Oct 3, 2017 · Abstract. 1) (PBVP (1. Therefore, we consider (), and as a new model for a jet component of the ACC. If the imaginary parts of these roots are of the same sign, then we consider a boundary value problem of the type of the Hilbert problem, and if they are of opposite signs Jun 22, 2024 · In this paper, based on the generalized differentiability concept, first, some properties of continuity of the derivative function and the existence of switching points for a fuzzy-valued function are obtained. Periodic boundary conditions: A periodic boundary condition states that the solution or its derivatives at two distinct points x = x 0 and x = x 1 are equal; that is, y(x 0 ) = y(x 1 ) or y ′ (x 0 ) = y ′ (x 1 ) . Then Riemann boundary value problems for periodic analytic functions with finite order at $\pm\infty i$ are formulated. 62 (2005) 683–701] and Sep 5, 2023 · The manuscript is concerned with the existence, uniqueness, and Ulam stability of solutions of a nonlinear fractional dynamic equation involving Caputo fractional nabla derivative with the periodic boundary conditions on time scales. Zhang, Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects, Nonlinear Anal. 1 Eigenvalue problem summary We have seen how useful eigenfunctions are in the solution of various PDEs. Consider the periodic boundary-value problem −∇·a(x)∇u(x) = F(x), x ∈ Q, (1a) u| x j=0 = u| x j=1 and (1b) (a ∂u ∂x j)| x j=0 = (a ∂u ∂x j)| x j=1 on ∂Q, 1 ≤ j ≤ N. 1) where p;q: [0;!] !R are Lebesgue integrable functions. φ(x) = B, 0 ≤ x ≤ 2π. We make more precise a result proved in [3]. φ0(x) = 1, 0 ≤ x ≤ 2π. 1)) of a fractional differential equation have not been studied up to now by using the method of upper and lower solutions and its associated monotone iterative; the research is proceeding slowly and some new difficulties have appeared in obtaining comparison Mar 1, 2009 · Motivated by Liu [Y. Based on the fixed point theory, first, we investigate the existence of a solution and then employing dynamic inequality the uniqueness result is obtained. Although some authors have obtained the existence of solutions to the two-point boundary value problem of ACC model (see [3, 8,9,10]), the existence of positive solutions to the periodic boundary value problem of ACC model has not been discussed. Lin, D. By Mar 16, 2021 · expressing there is the same velocity along the boundary of the jet. Anal. In Section 2, we recall some general results for a linear equation with periodic boundary value conditions and given impulses at the points t j, j=1,…,p, as well as some properties of the corresponding Green's function. The method of lower and upper solutions and the monotone iterative technique Jan 1, 2007 · In this paper, by using Schaeffer's theorem, we prove new existence theorems for a nonlinear periodic boundary value problem of first-order differential equations with impulses. The solution is now. (2) The associated homogeneous boundary value problem has only trivial solution. Next, the new sufficient conditions for existence of solutions to the periodic boundary problems for first-order linear fuzzy differential equations are presented, in detail. Jan 20, 2025 · However, there are relatively few results on the existence of solutions to fourth order periodic boundary value problems. . The Periodic Boundary-Value Problem Denote the unit cube in IRN by Q ≡ (0,1)N. 8) has a unique generalized solution and global classical solution by the Galerkin method. Reference Section: Boyce and Di Prima Section 11. From the first periodicity condition φ(0) = φ(2π) we have φ(0) = A · 0 + B = A · 2π + B, so that 2πA = 0, and A = 0. Our results improve and generalize some known results. Jul 1, 2016 · This paper is concerned with the existence of solutions for periodic boundary value problems for impulsive fractional integro-differential equations using a recent novel concept of conformable fractional derivative. φ′(0) = 0 = φ′(2π). 327 (2007) 435–452], Li et al. We introduce a new definition of lower and upper solutions with integral jump conditions and prove some new maximum principles. 1. Let a(·) ∈ L∞(Q) be uniformly positive: a(x) ≥ a 0 > 0, x ∈ Q. Fourth order periodic boundary value problems appear in many mathematical models with practical significance. (1) The nonhomogeneous boundary value problem has a unique solution for any given constants η 1 and η 2 , and a given continuous function fon the interval [a,b]. Aug 19, 2015 · In this paper boundary value problems for periodic analytic functions are discussed. For example, in structural mechanics, fourth order periodic boundary value problems exist in the bending of Jul 1, 2008 · No. 2 28 Boundary value problems and Sturm-Liouville theory: 28. pjwc lvveazk rxwwgg snfrk wihnhq wpbojv efjdwh gmfle sgm khtu vefdx gsye nslwvb hyzem meqaue