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JournalISSN: 1687-2762

Boundary Value Problems 

Springer Nature
About: Boundary Value Problems is an academic journal published by Springer Nature. The journal publishes majorly in the area(s): Partial differential equation & Ordinary differential equation. It has an ISSN identifier of 1687-2762. It is also open access. Over the lifetime, 2606 publications have been published receiving 20835 citations.


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Book ChapterDOI
TL;DR: In this article, the Riemann boundary value problem of analytic functions is discussed and the concept of the index of a function is discussed, which is of great value as an auxiliary tool.
Abstract: This chapter discusses the principal problem of the theory of boundary value problems of analytic functions namely the Riemann boundary value problem. It reviews the concept of the index of a function, which is of great value as an auxiliary tool. Various assertions are made in the chapter—(1) the index of a function that is continuous on a closed contour and does not vanish anywhere on it, is an integer or zero; the definition of the index immediately implies the statement, and (2) the index of a product of functions is equal to the sum of the indices of the factors. The index of a quotient is equal to the difference of the indices of the dividend and the divisor. The chapter also discusses the Riemann problem for a simply-connected domain, determination of sectionally analytic function in accordance with given jump, the canonical function of the homogeneous problem, the Riemann problem for the semi-plane, and Riemann boundary value problem with shift.

450 citations

Journal ArticleDOI
TL;DR: In this paper, the existence results for a boundary value problem involving a nonlinear integrodifferential equation of fractional order with integral boundary conditions are given for Krasnosel'skiĭ's fixed point theorem.
Abstract: This paper deals with some existence results for a boundary value problem involving a nonlinear integrodifferential equation of fractional order with integral boundary conditions. Our results are based on contraction mapping principle and Krasnosel'skiĭ's fixed point theorem.

212 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide an extension for the second-order differential equation of a thermostat model to the fractional hybrid equation and inclusion versions, where boundary value conditions of this problem in the form of the hybrid conditions are considered.
Abstract: We provide an extension for the second-order differential equation of a thermostat model to the fractional hybrid equation and inclusion versions. We consider boundary value conditions of this problem in the form of the hybrid conditions. To prove the existence of solutions for our hybrid fractional thermostat equation and inclusion versions, we apply the well-known Dhage fixed point theorems for single-valued and set-valued maps. Finally, we give two examples to illustrate our main results.

211 citations

Journal ArticleDOI
TL;DR: In this article, the existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained.
Abstract: The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

189 citations

Journal ArticleDOI
TL;DR: In this paper, the existence of solutions for two types of high order fractional integro-differential equations is studied. But the authors focus on the CFD and DCF derivations.
Abstract: By using the fractional Caputo–Fabrizio derivative, we introduce two types new high order derivations called CFD and DCF. Also, we study the existence of solutions for two such type high order fractional integro-differential equations. We illustrate our results by providing two examples.

168 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202379
2022170
202193
2020158
2019194
2018192