Kirchhoff-Type Boundary-Value Problems on the Real Line

2018 ◽  
pp. 141-153
Author(s):  
Shapour Heidarkhani ◽  
Amjad Salari ◽  
David Barilla
Keyword(s):  
Boundary Value Problems ◽  
Real Line ◽  
Boundary Value ◽  
The Real ◽  
Kirchhoff Type ◽  
Type Boundary

scholarly journals Non-autonomous boundary value problems on the real line

2006 ◽  
Vol 15 (3) ◽  
pp. 759-776 ◽  
Author(s):  
Barbara Bianconi ◽  
◽  
Francesca Papalini
Keyword(s):  
Boundary Value Problems ◽  
Real Line ◽  
Boundary Value ◽  
The Real

scholarly journals A critical point approach to boundary value problems on the real line

2018 ◽  
Vol 76 ◽  
pp. 215-220 ◽  
Author(s):  
Martin Bohner ◽  
Giuseppe Caristi ◽  
Shapour Heidarkhani ◽  
Shahin Moradi
Keyword(s):  
Boundary Value Problems ◽  
Critical Point ◽  
Real Line ◽  
Boundary Value ◽  
The Real

scholarly journals On the peakon inverse problem for the Degasperis-Procesi equation

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Keivan Mohajer
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Real Line ◽  
Boundary Value ◽  
The Real ◽  
String Type ◽  
Biorthogonal Polynomials ◽  
Type Boundary

Abstract The peakon inverse problem for the Degasperis-Procesi equation is solved directly on the real line, using Cauchy biorthogonal polynomials, without any additional transformation to a “string”-type boundary value problem known from prior works.

Hilbert boundary value problems—a distributional approach

1977 ◽  
Vol 77 (3-4) ◽  
pp. 193-208 ◽  
Author(s):  
Marion Orton
Keyword(s):  
Boundary Value Problems ◽  
Half Space ◽  
Open Subset ◽  
Real Line ◽  
Boundary Value ◽  
Growth Conditions ◽  
The Real ◽  
Singular Support ◽  
Schwartz Distributions ◽  
Finite Set

SynopsisHilbert boundary value problems for a half-space are considered for analytic representations of Schwartz distributions: given data g ∈D'(ℛ) and a coefficient x we seek functions F(z) analytic for Jmz≠0 whose limits exist in D'(ℛ) and satisfy F+—XF– = g on an open subset U of the real line R. U is the complement of a finite set which contains the singular support and the zeros of X·X and its reciprocal satisfy certain growth conditions near the boundary points of U. Solutions F(z) are shown to exist, and their general form is determined by obtaining a suitable factorisation of x.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary

Mixed type boundary value problems for Laplace–Beltrami equation on a surface with the Lipschitz boundary

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Roland Duduchava
Keyword(s):  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Beltrami Equation ◽  
Bessel Potential ◽  
Convolution Operators ◽  
Classical Setting ◽  
Type Boundary ◽  
Mellin Convolution ◽  
Bessel Potential Spaces

AbstractThe purpose of the present research is to investigate a general mixed type boundary value problem for the Laplace–Beltrami equation on a surface with the Lipschitz boundary 𝒞 in the non-classical setting when solutions are sought in the Bessel potential spaces \mathbb{H}^{s}_{p}(\mathcal{C}), \frac{1}{p}<s<1+\frac{1}{p}, 1<p<\infty. Fredholm criteria and unique solvability criteria are found. By the localization, the problem is reduced to the investigation of model Dirichlet, Neumann and mixed boundary value problems for the Laplace equation in a planar angular domain \Omega_{\alpha}\subset\mathbb{R}^{2} of magnitude 𝛼. The model mixed BVP is investigated in the earlier paper [R. Duduchava and M. Tsaava, Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain, Georgian Math. J.27 (2020), 2, 211–231], and the model Dirichlet and Neumann boundary value problems are studied in the non-classical setting. The problems are investigated by the potential method and reduction to locally equivalent 2\times 2 systems of Mellin convolution equations with meromorphic kernels on the semi-infinite axes \mathbb{R}^{+} in the Bessel potential spaces. Such equations were recently studied by R. Duduchava [Mellin convolution operators in Bessel potential spaces with admissible meromorphic kernels, Mem. Differ. Equ. Math. Phys.60 (2013), 135–177] and V. Didenko and R. Duduchava [Mellin convolution operators in Bessel potential spaces, J. Math. Anal. Appl.443 (2016), 2, 707–731].

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