Existence results for a non-homogeneous Neumann problem through Orlicz–Sobolev spaces

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Shapour Heidarkhani ◽  
Giuseppe Caristi ◽  
Ghasem A. Afrouzi ◽  
Shahin Moradi
Keyword(s):  
Weak Solution ◽  
Variational Principle ◽  
Sobolev Space ◽  
Banach Spaces ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Existence Results ◽  
Reflexive Banach Spaces

Abstract Based on a variational principle for smooth functionals defined on reflexive Banach spaces, the existence of at least one weak solution for a non-homogeneous Neumann problem in an appropriate Orlicz–Sobolev space is discussed.

scholarly journals Existence theorems for generalized vector equilibria with variable ordering relation

2016 ◽  
Vol 47 (4) ◽  
pp. 455-475
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Existence Theorems ◽  
Strong Solutions ◽  
Existence Results ◽  
Reflexive Banach Spaces ◽  
Fan Theorem ◽  
Variable Ordering ◽  
Vector Equilibrium

In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.

scholarly journals Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

2017 ◽  
Vol 3 (1) ◽  
pp. 70-82
Author(s):  
A. Ahmed ◽  
M.S.B. Elemine Vall ◽  
A. Touzani
Keyword(s):  
Variational Principle ◽  
Critical Point ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Elliptic Systems ◽  
Subject Classification ◽  
Infinitely Many Solutions ◽  
Variable Exponent Sobolev Spaces ◽  
The Neumann Problem

Abstract In this paper, we prove the existence of in finitely many solutions for the following system by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle and the theory of the anisotropic variable exponent Sobolev spaces 2010 Mathematics Subject Classification. 35K05 - 35K55.

Low-dimensional compact embeddings of symmetric Sobolev spaces with applications

2011 ◽  
Vol 141 (2) ◽  
pp. 383-395 ◽  
Author(s):  
Francesca Faraci ◽  
Antonio Iannizzotto ◽  
Alexandru Kristály
Keyword(s):  
Sobolev Space ◽  
Neumann Problem ◽  
Unbounded Domain ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Symmetric Functions ◽  
Laplacian Operator ◽  
Compact Embeddings ◽  
Cylindrically Symmetric ◽  
Low Dimensional

If Ω is an unbounded domain in ℝN and p > N, the Sobolev space W1,p(Ω) is not compactly embedded into L∈(Ω). Nevertheless, we prove that if Ω is a strip-like domain, then the subspace of W1,p(Ω) consisting of the cylindrically symmetric functions is compactly embedded into L∈(Ω). As an application, we study a Neumann problem involving the p-Laplacian operator and an oscillating nonlinearity, proving the existence of infinitely many weak solutions. Analogous results are obtained for the case of partial symmetry.

Two non-trivial solutions for a non-homogeneous Neumann problem: an Orlicz–Sobolev space setting

2009 ◽  
Vol 139 (2) ◽  
pp. 367-379 ◽  
Author(s):  
Alexandru Kristály ◽  
Mihai Mihăilescu ◽  
Vicenţiu Rădulescu
Keyword(s):  
Variational Principle ◽  
Sobolev Space ◽  
Neumann Problem ◽  
Growth Condition ◽  
Type Problem ◽  
Space Setting ◽  
Standard Growth Condition ◽  
Neumann Type

In this paper we study a non-homogeneous Neumann-type problem which involves a nonlinearity satisfying a non-standard growth condition. By using a recent variational principle of Ricceri, we establish the existence of at least two non-trivial solutions in an appropriate Orlicz–Sobolev space.

Existence results for a Kirchhoff type equation in Orlicz–Sobolev spaces

2017 ◽  
Vol 8 (3) ◽  
Author(s):  
EL Miloud Hssini ◽  
Najib Tsouli ◽  
Mustapha Haddaoui
Keyword(s):  
Variational Principle ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Type Equation ◽  
Existence Results ◽  
Mountain Pass ◽  
Nonlocal Problems ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

AbstractIn this paper, based on the mountain pass theorem and Ekeland’s variational principle, we show the existence of solutions for a class of non-homogeneous and nonlocal problems in Orlicz–Sobolev spaces.

scholarly journals Multiplicity of Solutions for Perturbed Nonhomogeneous Neumann Problem through Orlicz-Sobolev Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Liu Yang
Keyword(s):  
Sobolev Space ◽  
Variational Methods ◽  
Critical Point ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Sufficient Conditions ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Critical Point Theorems

We investigate the existence of multiple solutions for a class of nonhomogeneous Neumann problem with a perturbed term. By using variational methods and three critical point theorems of B. Ricceri, we establish some new sufficient conditions under which such a problem possesses three solutions in an appropriate Orlicz-Sobolev space.

scholarly journals Existence of solutions for a class of variational-hemivariational-like inequalities in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3609-3622
Author(s):  
Lu-Chuan Ceng ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Banach Spaces ◽  
Existence Of Solutions ◽  
Directional Derivative ◽  
Existence Results ◽  
Solution Set ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Gradient ◽  
Reflexive Banach Spaces ◽  
Necessary And Sufficient

This paper is devoted to study the existence of solutions for a class of variational-hemivariationallike inequalities in reflexive Banach spaces. Using the notion of the stable (?,?)-quasimonotonicity, the properties of Clarke?s generalized directional derivative and Clarke?s generalized gradient, we establish some existence results of solutions when the constrained set is nonempty, bounded (or unbounded), closed and convex. Moreover, a sufficient condition to the boundedness of the solution set and a necessary and sufficient condition to the existence of solutions are also derived.

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