scholarly journals Multiple Results to Some Biharmonic Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xingdong Tang ◽  
Jihui Zhang
Keyword(s):  
Elliptic Problem ◽  
Degree Theory ◽  
Critical Groups ◽  
Biharmonic Operator ◽  
Nonlinear Elliptic Problem ◽  
Topological Degree Theory ◽  
Nontrivial Solutions ◽  
Asymptotically Linear ◽  
Nonlinear Elliptic ◽  
Biharmonic Problems

We study a nonlinear elliptic problem defined in a bounded domain involving biharmonic operator together with an asymptotically linear term. We establish at least three nontrivial solutions using the topological degree theory and the critical groups.

scholarly journals Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian

2018 ◽  
Vol 20 (03) ◽  
pp. 1750032 ◽  
Author(s):  
Alexander Quaas ◽  
Aliang Xia
Keyword(s):  
Positive Solutions ◽  
Fractional Laplacian ◽  
Degree Theory ◽  
Elliptic Systems ◽  
Existence Results ◽  
Nonlinear Elliptic Problem ◽  
Topological Degree Theory ◽  
Scaling Method ◽  
Smooth Bounded Domain ◽  
Nonlinear Elliptic

In this paper, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: [Formula: see text] where [Formula: see text] denotes the fractional Laplacian and [Formula: see text] is a smooth bounded domain in [Formula: see text]. It shown that under some assumptions on [Formula: see text] and [Formula: see text], the problem has at least one positive solution [Formula: see text]. Our proof is based on the classical scaling method of Gidas and Spruck and topological degree theory.

scholarly journals Global Bifurcation of Positive Solutions of Asymptotically Linear Elliptic Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ruyun Ma ◽  
Yanqiong Lu ◽  
Ruipeng Chen
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Global Bifurcation ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problem ◽  
Asymptotically Linear ◽  
Bifurcation Theorem ◽  
Nonlinear Elliptic

We are concerned with determining values ofλ, for which there exist positive solutions of the nonlinear elliptic problem-Δu=λa(x)f(u)  in  Ω,∂u/∂n+b(x)g(u)=0  on  ∂Ω.The proof of our main results is based upon unilateral global bifurcation theorem of López-Gómez.

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 .

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