Non-Existence Results for a Semilinear Hyperbolic Problem with Boundary Condition of Memory Type

2000 ◽  
Vol 19 (2) ◽  
pp. 453-468 ◽  
Author(s):  
Mokhtar Kirane ◽  
Nasser-edine Tatar
Keyword(s):  
Boundary Condition ◽  
Existence Results ◽  
Hyperbolic Problem ◽  
Memory Type

scholarly journals On Periodic Fractional (p, q)-Integral Boundary Value Problems for Sequential Fractional (p, q)-Integrodifference Equations

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 264
Author(s):  
Jarunee Soontharanon ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Integral Boundary Condition ◽  
Integrodifference Equations ◽  
Integrodifference Equation ◽  
Integral Boundary ◽  
Integral Boundary Value Problems

We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (p, q)-integral are also presented in this paper as a tool for our calculations.

scholarly journals On sequential fractional Caputo $ (p, q) $-integrodifference equations via three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition

2021 ◽  
Vol 7 (1) ◽  
pp. 704-722
Author(s):  
Jarunee Soontharanon ◽  
◽  
Thanin Sitthiwirattham ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Integrodifference Equations ◽  
Integrodifference Equation

<abstract><p>In this paper, we aim to study the problem of a sequential fractional Caputo $ (p, q) $-integrodifference equation with three-point fractional Riemann-Liouville $ (p, q) $-difference boundary condition. We use some properties of $ (p, q) $-integral in this study and employ Banach fixed point theorems and Schauder's fixed point theorems to prove existence results of this problem.</p></abstract>

scholarly journals Weighted Steklov problem under nonresonance conditions

2018 ◽  
Vol 36 (4) ◽  
pp. 87-105
Author(s):  
Jonas Doumatè ◽  
Aboubacar Marcos
Keyword(s):  
Boundary Condition ◽  
Nonlinear Problem ◽  
Weak Solutions ◽  
Existence Results ◽  
Smooth Domain ◽  
Existence Of Weak Solutions ◽  
Steklov Problem ◽  
Bounded Smooth Domain ◽  
Carathéodory Function ◽  
Bounded Smooth

We deal with the existence of weak solutions of the nonlinear problem $-\Delta_{p}u+V|u|^{p-2}u$ in a bounded smooth domain $\Omega\subset \mathbb{R}^{N}$ which is subject to the boundary condition $|\nabla u|^{p-2}\frac{\partial u}{\partial \nu}=f(x,u)$. Here $V\in L^{\infty}(\Omega)$ possibly exhibit both signs which leads to an extension  of particular cases in literature and $f$ is a Carathéodory function that satisfies some additional conditions. Finally we prove, under and between nonresonance condtions, existence results for the problem.

scholarly journals Existence Results for the p(x)-Laplacian with Nonlinear Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhiqiang Wei ◽  
Zigao Chen
Keyword(s):  
Boundary Condition ◽  
Variational Method ◽  
Bounded Domain ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Existence Results ◽  
Global Minimizer ◽  
Fountain Theorem

By using the variational method, under appropriate assumptions on the perturbation terms such that the associated functional satisfies the global minimizer condition and the fountain theorem, respectively, the existence and multiple results for the -Laplacian with nonlinear boundary condition in bounded domain Ω were studied. The discussion is based on variable exponent Lebesgue and Sobolev spaces.

Existence Results of Mild Solutions for Impulsive Fractional Evolution Equations with Periodic Boundary Condition

2017 ◽  
Vol 18 (7-8) ◽  
pp. 585-598
Author(s):  
Baolin Li ◽  
Haide Gou
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Evolution Equations ◽  
Existence Theorems ◽  
Mild Solutions ◽  
Existence Results ◽  
Fractional Evolution Equations

AbstractThis paper discusses the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition and noncompact semigroup. By using some fixed-point theorems, the existence theorems of mild solutions are obtained, our results are also more general than known results. Furthermore, as an application that illustrates the abstract results, two examples are given.

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