scholarly journals Infinitely many weak solutions for a non-homogeneous Neumann problem in Orlicz--Sobolev spaces

2019 ◽  
Vol 60 (3) ◽  
pp. 361-378
Author(s):  
 Afrouzi Ghasem A. ◽  
Shokooh Shaeid ◽  
Chung Nguyen T.
Keyword(s):  
Neumann Problem ◽  
Sobolev Spaces ◽  
Weak Solutions

scholarly journals Poincaré Inequalities and Neumann Problems for the p-Laplacian

2018 ◽  
Vol 61 (4) ◽  
pp. 738-753 ◽  
Author(s):  
David Cruz-Uribe ◽  
Scott Rodney ◽  
Emily Rosta
Keyword(s):  
Quadratic Form ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Poincaré Inequalities ◽  
Existence Of Weak Solutions ◽  
Neumann Problems ◽  
Poincare Inequalities ◽  
Associated Matrix ◽  
Weighted Poincaré Inequalities

AbstractWe prove an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a Neumann problem related to a degenerate p-Laplacian. The Poincaré inequalities are formulated in the context of degenerate Sobolev spaces defined in terms of a quadratic form, and the associated matrix is the source of the degeneracy in the p-Laplacian.

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.

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 Three weak solutions for a Neumann elliptic equations involving the p→(x)\vec p\left( x \right)-Laplacian operator

2020 ◽  
Vol 7 (1) ◽  
pp. 224-236
Author(s):  
Ahmed Ahmed ◽  
Mohamed Saad Bouh Elemine Vall
Keyword(s):  
Neumann Problem ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Laplacian Operator ◽  
Variable Exponent Sobolev Spaces

AbstractThe aim of this paper is to establish the existence of at least three weak solutions for the following elliptic Neumann problem \left\{ {\matrix{ { - {\Delta _{\vec p\left( x \right)}}u + \alpha \left( x \right){{\left| u \right|}^{{p_0}\left( x \right) - 2}}u = \lambda f\left( {x,u} \right)} \hfill & {in} \hfill & {\Omega ,} \hfill \cr {\sum\limits_{i = 1}^N {{{\left| {{{\partial u} \over {\partial {x_i}}}} \right|}^{{p_i}\left( x \right) - 2}}{{\partial u} \over {\partial {x_i}}}{\gamma _i} = 0} } \hfill & {on} \hfill & {\partial \Omega ,} \hfill \cr } } \right. in the anisotropic variable exponent Sobolev spaces W1,\vec p\left( \cdot \right)\left( \Omega \right) where λ > 0 and f (x, t) = |t|q(x)−2t − |t|s(x)−2t, x ∈ Ω, t ∈ 𝕉 and q(·), s\left( \cdot \right) \in {\mathcal{C}_ + }\left( {\bar \Omega } \right).

scholarly journals Weak Solutions and Energy Estimates for a Class of Nonlinear Elliptic Neumann Problems

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Gabriele Bonanno ◽  
Giovanni Molica Bisci ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Neumann Problem ◽  
Laplace Operator ◽  
Weak Solutions ◽  
Existence Results ◽  
Energy Estimates ◽  
Lack Of Compactness ◽  
Neumann Problems ◽  
Estimates Of Solutions ◽  
Nonlinear Elliptic

AbstractWe establish existence results and energy estimates of solutions for a homogeneous Neumann problem involving the p-Laplace operator. The case of large dimensions, corresponding to the lack of compactness of W

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
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