scholarly journals On Weak Solvability of Boundary Value Problem with Variable Exponent Arising in Nanostructure

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Hicham Maadan ◽  
Nour Eddine Askour ◽  
Jamal Messaho
Keyword(s):  
Sobolev Space ◽  
Boundary Value Problem ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Variable Exponent ◽  
Boundary Value ◽  
Limit Problem ◽  
Limit Behavior ◽  
Interface Conditions ◽  
Weak Solvability

This work is devoted to study the limit behavior of weak solutions of an elliptic problem with variable exponent, in a containing structure, of an oscillating nanolayer of thickness and periodicity parameter depending on ε . The generalized Sobolev space is constructed, and the epiconvergence method is considered to find the limit problem with interface conditions.

Elliptic problems in generalized Orlicz-Musielak spaces

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Piotr Gwiazda ◽  
Piotr Minakowski ◽  
Aneta Wróblewska-Kamińska
Keyword(s):  
Boundary Value Problem ◽  
Banach Spaces ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Hölder Continuous ◽  
Existence Of Weak Solutions ◽  
Strongly Nonlinear

AbstractWe consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.

Critical points approaches to a nonlocal elliptic problem driven by 𝑝(𝑥)-biharmonic operator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shapour Heidarkhani ◽  
Shahin Moradi ◽  
Mustafa Avci
Keyword(s):  
Variational Methods ◽  
Elasticity Theory ◽  
Critical Points ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Variable Exponent ◽  
Electrorheological Fluids ◽  
Biharmonic Operator ◽  
Technical Approach ◽  
Nonlinear Elasticity Theory

Abstract Differential equations with variable exponent arise from the nonlinear elasticity theory and the theory of electrorheological fluids. We study the existence of at least three weak solutions for the nonlocal elliptic problems driven by p ⁢ ( x ) p(x) -biharmonic operator. Our technical approach is based on variational methods. Some applications illustrate the obtained results. We also provide an example in order to illustrate our main abstract results. We extend and improve some recent results.

EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 61 (3) ◽  
pp. 305-319
Author(s):  
CRISTIAN-PAUL DANET
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.

scholarly journals Entropy Solution for Doubly Nonlinear Elliptic Anisotropic Problems with Robin Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
I. Ibrango ◽  
S. Ouaro
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Boundary Value ◽  
Monotone Operators ◽  
Robin Boundary Conditions ◽  
Anisotropic Problems ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

We study in this paper nonlinear anisotropic problems with Robin boundary conditions. We prove, by using the technic of monotone operators in Banach spaces, the existence of a sequence of weak solutions of approximation problems associated with the anisotropic Robin boundary value problem. For the existence and uniqueness of entropy solutions, we prove that the sequence of weak solutions converges to a measurable function which is the entropy solution of the anisotropic Robin boundary value problem.

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