The Existence of a Generalized Solution of an $m$-Point Nonlocal Boundary Value Problem

David Devadze

Displaying similar documents to “The Existence of a Generalized Solution of an $m$ -Point Nonlocal Boundary Value Problem”

Existence Theorems for a Fourth Order Boundary Value Problem

A. El-Haffaf (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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This paper treats the question of the existence of solutions of a fourth order boundary value problem having the following form: $x^{(4)} (t) + f (t, x (t), x^{''} (t)) = 0$ , 0 < t < 1, x(0) = x’(0) = 0, x”(1) = 0, $x^{(3)} (1) = 0$ . Boundary value problems of very similar type are also considered. It is assumed that f is a function from the space C([0,1]×ℝ²,ℝ). The main tool used in the proof is the Leray-Schauder nonlinear alternative.

Boundary value problems with bounded $ϕ$ -Laplacian and nonlocal conditions of integral type

Daria Bugajewska, Jean Mawhin (2025)

Czechoslovak Mathematical Journal

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We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded $ϕ$ -Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals.

Boundary blow-up solutions for a cooperative system involving the p-Laplacian

Li Chen, Yujuan Chen, Dang Luo (2013)

Annales Polonici Mathematici

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We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $Δ_{p} u = g (u - α v), Δ_{p} v = f (v - β u)$ in a smooth bounded domain of $ℝ^{N}$ , where $Δ_{p}$ is the p-Laplacian operator defined by $Δ_{p} u = {d i v (| \nabla u |}^{p - 2} \nabla u)$ with p > 1, f and g are nondecreasing, nonnegative C¹ functions, and α and β are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for p = 2.

Characterizations of $H_{x} 1$ -sufficiency of jets

Le Tien Tam (1986)

Annales Polonici Mathematici

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Boundary value problems with compatible boundary conditions

George L. Karakostas, P. K. Palamides (2005)

Czechoslovak Mathematical Journal

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If $Y$ is a subset of the space $ℝ^{n} \times ℝ^{n}$ , we call a pair of continuous functions $U$ , $V$ $Y$ -compatible, if they map the space $ℝ^{n}$ into itself and satisfy $U x \cdot V y \geq 0$ , for all $(x, y) \in Y$ with $x \cdot y \geq 0$ . (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential $n$ -dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its...

Relations between the boundary values and periods for generalized analytic functions in $R^{n}$

Wolfgang Tutschke (1983)

Banach Center Publications

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Boundary values of functions in Cegrell’s class $_{ψ}$

Pham Hoang Hiep (2007)

Annales Polonici Mathematici

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We study boundary values of functions in Cegrell’s class $_{ψ}$ .

Continuous pluriharmonic boundary values

Per Åhag, Rafał Czyż (2007)

Annales Polonici Mathematici

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Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D ₁ \times \dots \times D_{s}$ , j=1,...,s, s≥ 3. Also let ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.

Vectorial quasilinear diffusion equation with dynamic boundary condition

Nakayashiki, Ryota

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In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S) $_{ε}$ with a nonnegative constant $ε$ , and for any $ε \geq 0$ , (S) $_{ε}$ can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain $Ω$ , and the parabolic equation on the boundary $Γ : = \partial Ω$ , having a sufficient smoothness. The objective of this study is to establish a mathematical method,...

Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain

M. Sango (2003)

Colloquium Mathematicae

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We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains $Q_{T}^{(s)}$ , s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of $Q_{T}^{(s)}$ . We give an explicit construction of that limit problem.

The basis property in $L_{p}$ of the boundary value problem rationally dependent on the eigenparameter

N. B. Kerimov, Y. N. Aliyev (2006)

Studia Mathematica

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We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in $L_{p}$ of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in L₂ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness...

On solutions of a fourth-order Lidstone boundary value problem at resonance

Mariusz Jurkiewicz (2009)

Annales Polonici Mathematici

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We consider a Lidstone boundary value problem in $ℝ^{k}$ at resonance. We prove the existence of a solution under the assumption that the nonlinear part is a Carathéodory map and conditions similar to those of Landesman-Lazer are satisfied.

Boundary value problem for an infinite system of second order differential equations in $ℓ_{p}$ spaces

Ishfaq Ahmad Malik, Tanweer Jalal (2020)

Mathematica Bohemica

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The concept of measures of noncompactness is applied to prove the existence of a solution for a boundary value problem for an infinite system of second order differential equations in $ℓ_{p}$ space. We change the boundary value problem into an equivalent system of infinite integral equations and result is obtained by using Darbo’s type fixed point theorem. The result is illustrated with help of an example.

Numerical approximation of the non-linear fourth-order boundary-value problem

Svobodová, Ivona

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We consider functionals of a potential energy $ℙ_{ψ} (u)$ corresponding to $𝑎𝑛 𝑎𝑥𝑖𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 - 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚$ . We are dealing with $𝑎 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑡ℎ𝑖𝑛 𝑎𝑛𝑛𝑢𝑙𝑎𝑟 𝑝𝑙𝑎𝑡𝑒$ with $𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠$ . Various types of the subsoil of the plate are described by various types of the $𝑛𝑜𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒$ nonlinear term $ψ (u)$ . The aim of the paper is to find a suitable computational algorithm.

Natural boundary value problems for weighted form laplacians

Wojciech Kozłowski, Antoni Pierzchalski (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The four natural boundary problems for the weighted form Laplacians $L = a d δ + b δ d, a, b > 0$ acting on polynomial differential forms in the $n$ -dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.

Existence of positive solutions for a nonlinear fourth order boundary value problem

Ruyun Ma (2003)

Annales Polonici Mathematici

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We study the existence of positive solutions of the nonlinear fourth order problem $u^{(4)} (x) = λ a (x) f (u (x))$ , u(0) = u’(0) = u”(1) = u”’(1) = 0, where a: [0,1] → ℝ may change sign, f(0) < 0, and λ < 0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.

Displaying similar documents to “The Existence of a Generalized Solution of an m -Point Nonlocal Boundary Value Problem”

Displaying similar documents to “The Existence of a Generalized Solution of an $m$ -Point Nonlocal Boundary Value Problem”