Existence of Nontrivial Solutions in Neumann Boundary Value Problems with Slow Principal Operators

Vy Khoi Le

doi:10.1007/s00025-008-0291-7

Existence of Nontrivial Solutions in Neumann Boundary Value Problems with Slow Principal Operators

Vy Khoi Le

Mathematics and Statistics

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Abstract

This paper is about the existence of nontrivial solutions of the Neumann boundary value problem{−div(a(|∇u|)∇u)=g(x,u)inΩ∂u/∂v=0on∂Ω, when the principal term has slow growth. Existence results of saddle points are based on recession arguments and variants of the Mountain Pass Theorem without Palais-Smale or Cerami condition in Orlicz-Sobolev spaces. Nontrivial solutions as global minimizers are also considered.

Original language	American English
Journal	Results in Mathematics
DOIs	https://doi.org/10.1007/s00025-008-0291-7
State	Published - Aug 1 2008

Keywords

Neumann boundary condition
Orlicz-Sobolev space
Variational inequality

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1007/s00025-008-0291-7

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title = "Existence of Nontrivial Solutions in Neumann Boundary Value Problems with Slow Principal Operators",

abstract = " This paper is about the existence of nontrivial solutions of the Neumann boundary value problem\{−div(a(|∇u|)∇u)=g(x,u)inΩ∂u/∂v=0on∂Ω, when the principal term has slow growth. Existence results of saddle points are based on recession arguments and variants of the Mountain Pass Theorem without Palais-Smale or Cerami condition in Orlicz-Sobolev spaces. Nontrivial solutions as global minimizers are also considered.",

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N2 - This paper is about the existence of nontrivial solutions of the Neumann boundary value problem{−div(a(|∇u|)∇u)=g(x,u)inΩ∂u/∂v=0on∂Ω, when the principal term has slow growth. Existence results of saddle points are based on recession arguments and variants of the Mountain Pass Theorem without Palais-Smale or Cerami condition in Orlicz-Sobolev spaces. Nontrivial solutions as global minimizers are also considered.

AB - This paper is about the existence of nontrivial solutions of the Neumann boundary value problem{−div(a(|∇u|)∇u)=g(x,u)inΩ∂u/∂v=0on∂Ω, when the principal term has slow growth. Existence results of saddle points are based on recession arguments and variants of the Mountain Pass Theorem without Palais-Smale or Cerami condition in Orlicz-Sobolev spaces. Nontrivial solutions as global minimizers are also considered.

KW - Neumann boundary condition

KW - Orlicz-Sobolev space

KW - Variational inequality

UR - https://scholarsmine.mst.edu/math_stat_facwork/496

UR - https://doi.org/10.1007/s00025-008-0291-7

U2 - 10.1007/s00025-008-0291-7

DO - 10.1007/s00025-008-0291-7

M3 - Article

JO - Results in Mathematics

JF - Results in Mathematics

ER -

Existence of Nontrivial Solutions in Neumann Boundary Value Problems with Slow Principal Operators

Abstract

Keywords

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