Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983 ◽  
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

scholarly journals New Existence and Uniqueness Results for Fractional Differential Equations

2013 ◽  
Vol 21 (3) ◽  
pp. 33-42 ◽  
Author(s):  
Ahmed Anber ◽  
Soumia Belarbi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper, we study a class of boundary value problems of nonlinear fractional differential equations with integral boundary conditions. Some new existence and uniqueness results are obtained by using Banach fixed point theorem. Other existence results are also presented by using Krasnoselskii theorem.

Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large

1994 ◽  
Vol 124 (1) ◽  
pp. 189-198 ◽  
Author(s):  
Zongming Guo ◽  
J. R. L. Webb
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Quasilinear Elliptic Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Quasilinear Elliptic

Existence and uniqueness results are proved for positive solutions of a class of quasilinear elliptic equations in a domain Ω⊂ℝN via a generalisation of Serrin's sweeping principle. In the case when Ω is an annulus, it is shown that the solution is radially symmetric.

Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Svatoslav Staněk
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Existence Results ◽  
Point Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Carathéodory Function ◽  
Fractional Differential

AbstractWe investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.

scholarly journals Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient

2021 ◽  
Vol 6 (1) ◽  
pp. 11
Author(s):  
Fang Li ◽  
Chenglong Wang ◽  
Huiwen Wang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Variable Coefficient ◽  
Existence Results ◽  
Initial Value ◽  
Hilfer Fractional Derivative ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

The aim of this paper is to establish the existence and uniqueness results for differential equations of Hilfer-type fractional order with variable coefficient. Firstly, we establish the equivalent Volterra integral equation to an initial value problem for a class of nonlinear fractional differential equations involving Hilfer fractional derivative. Secondly, we obtain the existence and uniqueness results for a class of Hilfer fractional differential equations with variable coefficient. We verify our results by providing two examples.

scholarly journals Existence and uniqueness results for an inverse problem for a semilinear equation with final overdetermination

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 847-858 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Abdullah Erdogan ◽  
Allaberen Ashyralyev
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Order Of Accuracy ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Semilinear Equation ◽  
Uniqueness Results

In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments.

scholarly journals Existence results for boundary value problems of arbitrary order integrodifferential equations in Banach spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 155-171 ◽  
Author(s):  
K. Karthikeyan ◽  
Bashir Ahmad
Keyword(s):  
Banach Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Caputo’S Derivative

Abstract We study a boundary value problem of fractional integrodifferential equations involving Caputo's derivative of order α ∈ (n-1,n) in a Banach space. Existence and uniqueness results for the problem are established by means of the Hölder's inequality together with some standard fixed point theorems

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