scholarly journals Existence and multiplicity of solutions for a class of quasilinear elliptic equations: An Orlicz–Sobolev space setting

2012 ◽  
Vol 389 (1) ◽  
pp. 420-428 ◽  
Author(s):  
Fei Fang ◽  
Zhong Tan
Keyword(s):  
Sobolev Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Multiplicity Of Solutions ◽  
Space Setting ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic

scholarly journals Existence and multiplicity results for quasilinear elliptic equations

2005 ◽  
Vol 71 (3) ◽  
pp. 377-386 ◽  
Author(s):  
Wei Dong
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Bounded Open Subset ◽  
Multiplicity Of Positive Solutions ◽  
Quasilinear Elliptic ◽  
Laplacian Operators

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f(x, s), we show the follwing problem: , where Ω is a bounded open subset of RN, N ≥ 2, with smooth boundary, λ is a positive parameter and ∆p is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large λ.

scholarly journals Existence and Multiplicity of Solutions for a Biharmonic Equation with p(x)-Kirchhoff Type

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Qi Zhang ◽  
Qing Miao
Keyword(s):  
Sobolev Space ◽  
Critical Point ◽  
Critical Point Theory ◽  
Elliptic Equations ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Point Theory ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity

Based on the basic theory and critical point theory of variable exponential Lebesgue Sobolev space, this paper investigates the existence and multiplicity of solutions for a class of nonlocal elliptic equations with Navier boundary value conditions when (AR) condition does not hold and improves or generalizes the original conclusions.

QUASILINEAR ELLIPTIC EQUATIONS OF THE HENON-TYPE: EXISTENCE OF NON-RADIAL SOLUTIONS

2009 ◽  
Vol 11 (05) ◽  
pp. 783-798 ◽  
Author(s):  
P. C. CARRIÃO ◽  
D. G. DE FIGUEIREDO ◽  
O. H. MIYAGAKI
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Quasilinear Elliptic Equations ◽  
Open Ball ◽  
Radial Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

In this work, we prove results on existence and multiplicity of non-radial solutions for a class of singular quasilinear elliptic problems of the form [Formula: see text] where B = {x ∈ ℝN: |x| < 1} (N ≥ 3) is a unit open ball centered at the origin, -∞ < a < (N - p)/p, β > 0 and [Formula: see text].

Existence and Multiplicity of Nontrivial Solutions to Quasilinear Elliptic Equations

2016 ◽  
Vol 16 (4) ◽  
Author(s):  
Anran Li ◽  
Chongqing Wei
Keyword(s):  
Morse Theory ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic

AbstractIn this paper, Morse theory is used to study the existence and multiplicity of nontrivial solutions for the following class of quasilinear elliptic equations:where

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