scholarly journals Existence of multiple solutions for a quasilinear elliptic problem

2017 ◽  
Vol 49 (2) ◽  
pp. 1
Author(s):  
Jorge Cossio ◽  
Sigifredo Herrón ◽  
Carlos Vélez
Keyword(s):  
Elliptic Problem ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

An existence result for multiple solutions to a Dirichlet problem

2017 ◽  
Vol 24 (1) ◽  
pp. 55-62
Author(s):  
Saeid Shokooh ◽  
Ghasem A. Afrouzi ◽  
John R. Graef
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Existence Result ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Three Solutions ◽  
Quasilinear Elliptic Problem ◽  
Critical Point Result ◽  
Quasilinear Elliptic

AbstractThe authors establish the existence of at least three solutions to a quasilinear elliptic problem subject to Dirichlet boundary conditions in a bounded domain in ${\mathbb{R}^{N}}$. A critical point result for differentiable functionals is used to prove the results.

scholarly journals Multiple solutions for a coercive quasilinear elliptic equation via Morse theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lifang Fu ◽  
Mingzheng Sun
Keyword(s):  
Elliptic Equation ◽  
Elliptic Problem ◽  
Morse Theory ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Nontrivial Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

AbstractWe study the quasilinear elliptic problem which is resonant at zero. By using Morse theory, we obtain five nontrivial solutions for the equation with coercive nonlinearities.

BOUNDED MULTIPLE SOLUTIONS FOR -LAPLACIAN PROBLEMS WITH ARBITRARY PERTURBATIONS

2015 ◽  
Vol 99 (2) ◽  
pp. 175-185 ◽  
Author(s):  
FRANCESCA FARACI ◽  
LIN ZHAO
Keyword(s):  
Elliptic Problem ◽  
Multiple Solutions ◽  
Abstract Result ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Iteration Technique

In the present paper we deal with the existence of multiple solutions for a quasilinear elliptic problem involving an arbitrary perturbation. Our approach, based on an abstract result of Ricceri, combines truncation arguments with Moser-type iteration technique.

MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS

2003 ◽  
Vol 05 (05) ◽  
pp. 737-759 ◽  
Author(s):  
NOBUYOSHI FUKAGAI ◽  
KIMIAKI NARUKAWA
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Eigenvalue Problems ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Nonlinear Eigenvalue Problems ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Nonlinear Eigenvalue

This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.

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