scholarly journals Dirichlet Problem for Maximal Graphs of Higher Codimension

2020 ◽  
Author(s):  
Yang Li
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
General Existence

Abstract We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian-type ambient spaces and obtain general existence and uniqueness results that apply to any codimension.

scholarly journals On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1899
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Liouville Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

scholarly journals Existence of Solution to a Second-Order Boundary Value Problem via Noncompactness Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wen-Xue Zhou ◽  
Jigen Peng
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Dirichlet Boundary ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Of Solution ◽  
Dirichlet Boundary Value Problem ◽  
Condensing Mapping

The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.

scholarly journals Existence and uniqueness results for a class of fractional differential equations with an integral fractional boundary condition

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1241-1249 ◽  
Author(s):  
Asghar Ahmadkhanlu
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Necessary Conditions ◽  
Boundary Value ◽  
Fractional Order Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Sufficient And Necessary Conditions ◽  
Fractional Differential

The aim of this work is to study a class of boundary value problem including a fractional order differential equation. Sufficient and necessary conditions will be presented for the existence and uniqueness of solution of this fractional boundary value problem.

scholarly journals Existence and uniqueness results for fractional Navier boundary value problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Imed Bachar ◽  
Hassan Eltayeb
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Operator Equation ◽  
Real Function ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Alpha Beta

Abstract We establish the existence, uniqueness, and positivity for the fractional Navier boundary value problem: $$\begin{aligned} \textstyle\begin{cases} D^{\alpha }(D^{\beta }\omega )(t)=h(t,\omega (t),D^{\beta }\omega (t)), & 0< t< 1, \\ \omega (0)=\omega (1)=D^{\beta }\omega (0)=D^{\beta }\omega (1)=0, \end{cases}\displaystyle \end{aligned}$$ { D α ( D β ω ) ( t ) = h ( t , ω ( t ) , D β ω ( t ) ) , 0 < t < 1 , ω ( 0 ) = ω ( 1 ) = D β ω ( 0 ) = D β ω ( 1 ) = 0 , where $\alpha,\beta \in (1,2]$ α , β ∈ ( 1 , 2 ] , $D^{\alpha }$ D α and $D^{\beta }$ D β are the Riemann–Liouville fractional derivatives. The nonlinear real function h is supposed to be continuous on $[0,1]\times \mathbb{R\times R}$ [ 0 , 1 ] × R × R and satisfy appropriate conditions. Our approach consists in reducing the problem to an operator equation and then applying known results. We provide an approximation of the solution. Our results extend those obtained in (Dang et al. in Numer. Algorithms 76(2):427–439, 2017) to the fractional setting.

Second order BVPs with state dependent impulses via lower and upper functions

2014 ◽  
Vol 12 (1) ◽  
Author(s):  
Irena Rachůnková ◽  
Jan Tomeček
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Dirichlet Boundary Value Problem ◽  
State Dependent ◽  
Lower And Upper Functions

AbstractThe paper deals with the following second order Dirichlet boundary value problem with p ∈ ℕ state-dependent impulses: z″(t) = f (t,z(t)) for a.e. t ∈ [0, T], z(0) = z(T) = 0, z′(τ i+) − z′(τ i−) = I i(τ i, z(τ i)), τ i = γ i(z(τ i)), i = 1,..., p. Solvability of this problem is proved under the assumption that there exists a well-ordered couple of lower and upper functions to the corresponding Dirichlet problem without impulses.

About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations

2003 ◽  
Vol 10 (3) ◽  
pp. 495-502
Author(s):  
Alexander Domoshnitsky
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Asymptotic Properties ◽  
Dirichlet Boundary Value Problem ◽  
The Maximum Principle ◽  
Unbounded Solutions ◽  
All Solutions

Abstract In this paper, oscillation and asymptotic properties of solutions of the Dirichlet boundary value problem for hyperbolic and parabolic equations are considered. We demonstrate that introducing an arbitrary constant delay essentially changes the above properties. For instance, the delay equation does not inherit the classical properties of the Dirichlet boundary value problem for the heat equation: the maximum principle is not valid, unbounded solutions appear while all solutions of the classical Dirichlet problem tend to zero at infinity, for “narrow enough zones” all solutions oscillate instead of being positive. We establish that the Dirichlet problem for the wave equation with delay can possess unbounded solutions. We estimate zones of positivity of solutions for hyperbolic equations.

scholarly journals On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 476
Author(s):  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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