scholarly journals Multiple solutions for quasilinear elliptic Neumann problems in Orlicz-Sobolev spaces

2005 ◽  
Vol 2005 (3) ◽  
pp. 872407 ◽  
Author(s):  
Nikolaos Halidias ◽  
Vy K Le
Keyword(s):  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Neumann Problems ◽  
Quasilinear Elliptic

Existence of multiple solutions of critical quasilinear elliptic Neumann problems

2000 ◽  
Vol 42 (4) ◽  
pp. 613-629 ◽  
Author(s):  
Paul A. Binding ◽  
Pavel Drábek ◽  
Yin Xi Huang
Keyword(s):  
Multiple Solutions ◽  
Neumann Problems ◽  
Quasilinear Elliptic

scholarly journals Existence of renormalized solutions for some quasilinear elliptic Neumann problems

2021 ◽  
Vol 8 (1) ◽  
pp. 180-206
Author(s):  
Mohamed Badr Benboubker ◽  
Hassane Hjiaj ◽  
Idrissa Ibrango ◽  
Stanislas Ouaro
Keyword(s):  
Sobolev Spaces ◽  
Variable Exponent ◽  
Growth Conditions ◽  
Renormalized Solutions ◽  
Neumann Problems ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Carathéodory Functions ◽  
Variable Exponent Sobolev Spaces ◽  
Quasilinear Elliptic

Abstract This paper is devoted to study some nonlinear elliptic Neumann equations of the type { A u + g ( x , u , ∇ u ) + | u | q ( ⋅ ) - 2 u = f ( x , u , ∇ u ) in Ω , ∑ i = 1 N a i ( x , u , ∇ u ) ⋅ n i = 0 on ∂ Ω , \left\{ {\matrix{ {Au + g(x,u,\nabla u) + |u{|^{q( \cdot ) - 2}}u = f(x,u,\nabla u)} \hfill & {{\rm{in}}} \hfill & {\Omega ,} \hfill \cr {\sum\limits_{i = 1}^N {{a_i}(x,u,\nabla u) \cdot {n_i} = 0} } \hfill & {{\rm{on}}} \hfill & {\partial \Omega ,} \hfill \cr } } \right. in the anisotropic variable exponent Sobolev spaces, where A is a Leray-Lions operator and g(x, u, ∇u), f (x, u, ∇u) are two Carathéodory functions that verify some growth conditions. We prove the existence of renormalized solutions for our strongly nonlinear elliptic Neumann problem.

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 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.

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