scholarly journals Variational Methods for a Fractional Dirichlet Problem Involving Jumarie’s Derivative

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Rafał Kamocki
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Existence And Uniqueness ◽  
Fundamental Lemma ◽  
Du Bois ◽  
Uniqueness Of A Solution

We investigate a fractional Dirichlet problem involving Jumarie’s derivative. Using some variational methods a theorem on the existence and uniqueness of a solution to such problem is proved. In the proof of the main result we use a fractional counterpart of the du Bois-Reymond fundamental lemma.

scholarly journals Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1352
Author(s):  
Jean Mawhin ◽  
Ewa Skrzypek ◽  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Time Scale ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Mountain Pass ◽  
Du Bois

This paper is devoted to study the existence of solutions and their regularity in the p(t)– Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois–Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

RANDOM DIFFERENTIAL EQUATIONS WITH RANDOM DELAYS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 369-388 ◽  
Author(s):  
M. J. GARRIDO-ATIENZA ◽  
A. OGROWSKY ◽  
B. SCHMALFUSS
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Random Dynamical System ◽  
Random Delay ◽  
Random Differential Equation ◽  
Autonomous Case ◽  
Random Differential Equations ◽  
Uniqueness Of A Solution

We investigate a random differential equation with random delay. First the non-autonomous case is considered. We show the existence and uniqueness of a solution that generates a cocycle. In particular, the existence of an attractor is proved. Secondly we look at the random case. We pay special attention to the measurability. This allows us to prove that the solution to the random differential equation generates a random dynamical system. The existence result of the attractor can be carried over to the random case.

Multiple Solutions to (p,q)-Laplacian Problems with Resonant Concave Nonlinearity

2016 ◽  
Vol 16 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Salvatore A. Marano ◽  
Sunra J. N. Mosconi ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Morse Theory ◽  
Multiple Solutions ◽  
First Eigenvalue ◽  
Reaction Term ◽  
The First Eigenvalue

AbstractThe existence of multiple solutions to a Dirichlet problem involving the ${(p,q)}$-Laplacian is investigated via variational methods, truncation-comparison techniques, and Morse theory. The involved reaction term is resonant at infinity with respect to the first eigenvalue of ${-\Delta_{p}}$ in ${W^{1,p}_{0}(\Omega)}$ and exhibits a concave behavior near zero.

scholarly journals On a Nonlinear Wave Equation of Kirchhoff-Carrier Type: Linear Approximation and Asymptotic Expansion of Solution in a Small Parameter

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Nguyen Huu Nhan ◽  
Le Thi Phuong Ngoc ◽  
Nguyen Thanh Long
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Weak Solution ◽  
Dirichlet Problem ◽  
Small Parameter ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Existence And Uniqueness ◽  
Linearization Method ◽  
Asymptotic Expansion Of Solution

We consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

scholarly journals Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Imed Bachar ◽  
Habib Mâagli
Keyword(s):  
Dirichlet Problem ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Nonlinear Effects ◽  
Weight Functions ◽  
Global Behavior ◽  
Bounded Domains ◽  
Euclidian Distance ◽  
Nonnegative Weight

We prove the existence and uniqueness of a positive continuous solution to the following singular semilinear fractional Dirichlet problem(-Δ)α/2u=a1(x)uσ1+a2(x)uσ2, in D  limx→z∈∂D(δ(x))1-(α/2)u(x)=0,where0<α<2, σ1,  σ2∈(-1,1), Dis a boundedC1,1-domain inℝn,n≥2,andδ(x)denotes the Euclidian distance fromxto the boundary ofD.The nonnegative weight functionsa1,  a2are required to satisfy certain hypotheses related to the Karamata class. We also investigate the global behavior of such solution.

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