Multiplicity of weak solutions to non-local elliptic equations involving the fractional p(x)-Laplacian

2020 ◽  
Vol 61 (1) ◽  
pp. 011505 ◽  
Author(s):  
Jun Ik Lee ◽  
Jae-Myoung Kim ◽  
Yun-Ho Kim ◽  
Jongrak Lee
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Non Local

scholarly journals On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskiĭ condition

1988 ◽  
Vol 11 (1) ◽  
pp. 101-113 ◽  
Author(s):  
J. H. Chabrowski
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Space ◽  
Boundary Value ◽  
Linear Elliptic Equation ◽  
Crucial Point ◽  
Non Local ◽  
Suitable Modification

In this paper we investigate the solvability of a non-local problem for a linear elliptic equation, which is also known as the boundary value problem with the Bitsadze-Samarskiĭ condition. We prove the existence and uniqueness of a classical solution to this problem. In the final part of this paper we propose anL2-approach which gives a rise to weak solutions in a weighted Sobolev space. The crucial point in proving the existence of weak solutions is a suitable modification of the Bitsadze-Samarskiĭ condition.

scholarly journals Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

scholarly journals Multiple of Solutions for Nonlocal Elliptic Equations with Critical Exponent Driven by the Fractional p-Laplacian of Order s

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
M. Khiddi
Keyword(s):  
Variational Methods ◽  
Critical Exponent ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Nehari Manifold ◽  
Lusternik Schnirelmann ◽  
The Nehari Manifold

In this paper, we study the existence of infinitely many weak solutions for nonlocal elliptic equations with critical exponent driven by the fractional p-Laplacian of order s. We show the above result when λ>0 is small enough. We achieve our goal by making use of variational methods, more specifically, the Nehari Manifold and Lusternik-Schnirelmann theory.

Radiative effects for some bidimensional thermoelectric problems

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Luisa Consiglieri
Keyword(s):  
Steady State ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Divergence Form ◽  
Radiative Effects ◽  
Existence Of Weak Solutions ◽  
Nonlinear Radiation ◽  
Radiation Type

AbstractThere are two main objectives in this paper. One is to find sufficient conditions to ensure the existence of weak solutions for some bidimensional thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at least a nonempty part of the boundary of a

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