A Multiplicity Result Including Sign-Changing Solutions For a Nonlinear Elliptic Problem in RN

2007 ◽  
Vol 7 (4) ◽  
Author(s):  
Norimichi Hirano ◽  
Naoki Shioji
Keyword(s):  
Elliptic Problem ◽  
Multiple Solutions ◽  
Multiplicity Result ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic ◽  
Sign Changing Solutions

AbstractWe show that the problemhas multiple solutions including sign-changing ones, where μ > 0, N ≥ 3, 1 < p < (N + 2)/(N − 2) and Q : ℝ

scholarly journals On the Existence of Nodal Solutions for a Nonlinear Elliptic Problem on Symmetric Riemannian Manifolds

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Anna Maria Micheletti ◽  
Angela Pistoia
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Elliptic Problem ◽  
Multiplicity Result ◽  
Nonlinear Elliptic Problem ◽  
Nodal Solutions ◽  
Nonlinear Elliptic ◽  
Sign Changing Solutions

Given thatis a smooth compact and symmetric Riemannian -manifold, , we prove a multiplicity result for antisymmetric sign changing solutions of the problem in . Here if and if .

Nonexistence Results of Sign-changing solutions for a Supercritical Problem of the Scalar Curvature Type

2012 ◽  
Vol 12 (1) ◽  
Author(s):  
Kamal Ould Bouh
Keyword(s):  
Critical Exponent ◽  
Scalar Curvature ◽  
Elliptic Problem ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic ◽  
Sign Changing Solutions ◽  
Supercritical Problem ◽  
Curvature Type

AbstractThis paper is devoted to the study of the nonlinear elliptic problem with supercritical critical exponent (P

scholarly journals A concave—convex elliptic problem involving the fractional Laplacian

2013 ◽  
Vol 143 (1) ◽  
pp. 39-71 ◽  
Author(s):  
C. Brändle ◽  
E. Colorado ◽  
A. de Pablo ◽  
U. Sánchez
Keyword(s):  
Elliptic Problem ◽  
Fractional Laplacian ◽  
Laplacian Operator ◽  
Multiplicity Result ◽  
Nonlinear Elliptic Problem ◽  
Trace Inequality ◽  
Fractional Powers ◽  
Liouville Type ◽  
Nonlinear Elliptic ◽  
Liouville Type Results

We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave—convex term. We completely characterize the range of parameters for which solutions of the problem exist and prove a multiplicity result. We also prove an associated trace inequality and some Liouville-type results.

PROFILE AND EXISTENCE OF SIGN-CHANGING SOLUTIONS TO AN ELLIPTIC SUBCRITICAL EQUATION

2008 ◽  
Vol 10 (06) ◽  
pp. 1183-1216 ◽  
Author(s):  
MOHAMED BEN AYED ◽  
RABEH GHOUDI
Keyword(s):  
Critical Exponent ◽  
Elliptic Problem ◽  
Blow Up ◽  
Low Energy ◽  
Nonlinear Elliptic Problem ◽  
Smooth Bounded Domain ◽  
Nonlinear Elliptic ◽  
Robin Function ◽  
Sign Changing Solutions ◽  
Two Bubbles

In this paper, we study the nonlinear elliptic problem involving nearly critical exponent (Pε) : Δ2 u = |u|(8/(n-4))-εu, in Ω, Δu = u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 5. We characterize the low energy sign-changing solutions (uε) of (Pε). We prove that (uε) are close to two bubbles with different signs and they have to blow up either at two different points with the same speed or at a critical point of the Robin function. Furthermore, we construct families of each kind of these solutions and we prove that the bubble-tower solutions exist in our case.

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