scholarly journals A nonexistence result for a nonlinear elliptic equation with singular and decaying potential

2015 ◽  
Vol 17 (04) ◽  
pp. 1450024 ◽  
Author(s):  
Marino Badiale ◽  
Michela Guida ◽  
Sergio Rolando
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Nonlinear Elliptic Equation ◽  
Negative Answer ◽  
Radial Solutions ◽  
Compatibility Conditions ◽  
Nonlinear Elliptic ◽  
Nonexistence Result ◽  
Open Case ◽  
Existence And Nonexistence

Several existence and nonexistence results are known for positive solutions u ∈ D1,2(ℝN) ∩ L2(ℝN, ∣x∣-αdx) ∩ Lp(ℝN) to the equation [Formula: see text] resting upon compatibility conditions between α and p. Letting 2α := 2N/(N - α) and [Formula: see text], the problem is still open for 0 < α < 2 and [Formula: see text], for 2 < α < N and [Formula: see text], and for N ≤ α < 2N - 2 and [Formula: see text]. Here we give a negative answer to the problem of the existence of radial solutions in the first open case.

scholarly journals Multiple solutions to a nonlinear elliptic equation involving Paneitz type operators

2004 ◽  
Vol 2004 (46) ◽  
pp. 2453-2472
Author(s):  
Abdallah El Hamidi
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Riemannian Manifolds ◽  
Multiple Solutions ◽  
Nonlinear Elliptic Equation ◽  
Existence Results ◽  
Real Parameter ◽  
Nonlinear Elliptic ◽  
Existence Of Positive Solutions ◽  
Characteristic Values

This paper deals with an elliptic equation involving Paneitz type operators on compact Riemannian manifolds with concave-convex nonlinearities and a real parameter. Nonlocal and multiple existence results are established. Characteristic values of the real parameter are introduced and their role in the change of the energy sign and the existence of positive solutions are highlighted.

Positive solutions for the Robin p-Laplacian problem with competing nonlinearities

2019 ◽  
Vol 12 (1) ◽  
pp. 31-56 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Nonlinear Elliptic Equation ◽  
Differential Operators ◽  
Comparison Principles ◽  
Reaction Term ◽  
Nonlinear Elliptic ◽  
Carathéodory Function ◽  
Concave And Convex Terms

AbstractWe consider a parametric nonlinear elliptic equation driven by the Robin p-Laplacian. The reaction term is a Carathéodory function which exhibits competing nonlinearities (concave and convex terms). We prove two bifurcation-type results describing the set of positive solutions as the parameter varies. In the process we also prove two strong comparison principles for Robin equations. These results are proved for differential operators which are more general than the p-Laplacian and need not be homogeneous.

scholarly journals Existence of positive solutions for some polyharmonic nonlinear equations inℝn

2006 ◽  
Vol 2006 ◽  
pp. 1-24 ◽  
Author(s):  
Habib Mâagli ◽  
Malek Zribi
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Equations ◽  
Positive Solutions ◽  
Nonlinear Elliptic Equation ◽  
Existence Results ◽  
Nonlinear Elliptic ◽  
Existence Of Positive Solutions ◽  
Class Of Functions

We will study the following polyharmonic nonlinear elliptic equation(−∆)mu+f(‧,u)=0inℝn,n>2m. Under appropriate conditions on the nonlinearityf(x,t), related to a class of functions calledm-Green-tight functions, we give some existence results for the above equation.

Sign in / Sign up

Export Citation Format

Share Document