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.

Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces

2018 ◽  
Vol 68 (4) ◽  
pp. 867-880
Author(s):  
Saeid Shokooh ◽  
Ghasem A. Afrouzi ◽  
John R. Graef
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Neumann Problems

Abstract By using variational methods and critical point theory in an appropriate Orlicz-Sobolev setting, the authors establish the existence of infinitely many non-negative weak solutions to a non-homogeneous Neumann problem. They also provide some particular cases and an example to illustrate the main results in this paper.

scholarly journals Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz–Sobolev spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Heidari ◽  
A. Razani
Keyword(s):  
Variational Methods ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Elliptic Systems ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

AbstractIn this paper, we study some results on the existence and multiplicity of solutions for a class of nonlocal quasilinear elliptic systems. In fact, we prove the existence of precise intervals of positive parameters such that the problem admits multiple solutions. Our approach is based on variational methods.

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

Existence of three solutions for a non-homogeneous Neumann problem through Orlicz–Sobolev spaces

2011 ◽  
Vol 74 (14) ◽  
pp. 4785-4795 ◽  
Author(s):  
Gabriele Bonanno ◽  
Giovanni Molica Bisci ◽  
Vicenţiu Rădulescu
Keyword(s):  
Neumann Problem ◽  
Sobolev Spaces ◽  
Three Solutions

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.

Multiple Solutions for Nonlinear Neumann Problems with Asymmetric Reaction, via Morse Theory

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Variational Methods ◽  
Neumann Problem ◽  
Morse Theory ◽  
Multiple Solutions ◽  
Smooth Solutions ◽  
Asymmetric Reaction ◽  
Neumann Problems ◽  
Nonlinear Neumann Problem ◽  
Asymmetric Behaviour ◽  
Nonlinear Neumann Problems

AbstractWe consider a nonlinear Neumann problem driven by the p-Laplacian and with a reaction which exhibits an asymmetric behaviour near +∞ and near −∞. Namely, it is (p − 1)- superlinear near +∞ (but need not satisfy the Ambrosetti-Rabinowitz condition) and it is (p − 1)-linear near −∞. Combining variational methods with Morse theory, we show that the problem has at least three nontrivial smooth solutions.

scholarly journals Multiple Solutions of Second-Order Damped Impulsive Differential Equations with Mixed Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jian Liu ◽  
Lizhao Yan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Mixed Boundary ◽  
Impulsive Differential Equations ◽  
Mixed Boundary Conditions ◽  
Second Order ◽  
Multiplicity Of Solutions

We use variational methods to investigate the solutions of damped impulsive differential equations with mixed boundary conditions. The conditions for the multiplicity of solutions are established. The main results are also demonstrated with examples.

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.

scholarly journals Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains

2005 ◽  
Vol 2005 (2) ◽  
pp. 185-205
Author(s):  
Michinori Ishiwata
Keyword(s):  
Elliptic Equations ◽  
Multiple Solutions ◽  
Point Of View ◽  
Semilinear Elliptic Equations ◽  
Singularly Perturbed ◽  
Bounded Domains ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Semilinear Elliptic ◽  
The Relationship

We are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domainsΩ:−ε2Δu+a(⋅)u=u|u|p−2inΩ,u>0inΩ,u=0on∂Ω. The main purpose of this paper is to discuss the relationship between the multiplicity of solutions and the profile ofa(⋅)from the variational point of view. It is shown that ifahas a “peak” inΩ, then (P) has at least three solutions for sufficiently smallε.

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