scholarly journals Nontrivial Solutions for a System of Fractional q-Difference Equations Involving q-Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 828 ◽  
Author(s):  
Yaohong Li ◽  
Jie Liu ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Integral Boundary Conditions ◽  
Integral Operators ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Integral Boundary ◽  
The First Eigenvalue ◽  
Linear Integral ◽  
Linear Integral Operators

In this paper, we study the existence of nontrivial solutions for a system of fractional q-difference equations involving q-integral boundary conditions, and we use the topological degree to establish our main results by considering the first eigenvalue of some associated linear integral operators.

scholarly journals On a class of semilinear elliptic equations with boundary conditions and potentials which change sign

2005 ◽  
Vol 2005 (2) ◽  
pp. 95-104
Author(s):  
M. Ouanan ◽  
A. Touzani
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Elliptic Equations ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Bounded Smooth Domain ◽  
The First Eigenvalue ◽  
Semilinear Elliptic ◽  
Superlinear Growth ◽  
Bounded Smooth

We study the existence of nontrivial solutions for the problemΔu=u, in a bounded smooth domainΩ⊂ℝℕ, with a semilinear boundary condition given by∂u/∂ν=λu−W(x)g(u), on the boundary of the domain, whereWis a potential changing sign,ghas a superlinear growth condition, and the parameterλ∈]0,λ1];λ1is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.

scholarly journals Sequential Derivatives of Nonlinearq-Difference Equations with Three-Pointq-Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nittaya Pongarm ◽  
Suphawat Asawasamrit ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Quantum Numbers ◽  
Derivatives Of

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinearq-difference equations with three-pointq-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.

scholarly journals A Study of Nonlinear Fractionalq-Difference Equations with Nonlocal Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Hana Al-Hutami
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractionalq-difference equations with nonlocal integral boundary conditions. The existence results are obtained by applying some well-known fixed point theorems and illustrated with examples.

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