Existence of positive solutions for Hardy nonlocal fractional elliptic equations involving critical nonlinearities

2019 ◽  
pp. 1 ◽  
Author(s):  
Somayeh Rastegarzadeh ◽  
Nemat Nyamoradi
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Critical Nonlinearities ◽  
Existence Of Positive Solutions

Elliptic equations with critical nonlinearities and Hardy terms

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Mohammed Bouchekif ◽  
Yasmina Nasri
Keyword(s):  
Elliptic Equation ◽  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Critical Nonlinearities ◽  
Existence Of Positive Solutions ◽  
Inverse Square Potentials

AbstractUsing variational methods, we prove the existence of positive solutions to an elliptic equation involving critical nonlinearities and multiple inverse square potentials.

Fractional elliptic equations with critical exponential nonlinearity

2016 ◽  
Vol 5 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Jacques Giacomoni ◽  
Pawan Kumar Mishra ◽  
K. Sreenadh
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Fractional Laplacian ◽  
Nehari Manifold ◽  
Mountain Pass ◽  
Laplacian Operator ◽  
Exponential Nonlinearity ◽  
Existence Of Positive Solutions ◽  
Fractional Laplacian Operator

AbstractWe study the existence of positive solutions for fractional elliptic equations of the type (-Δ)1/2u = h(u), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1) where h is a real valued function that behaves like eu2 as u → ∞ . Here (-Δ)1/2 is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near t = 0. In case h is concave near t = 0, we show the existence of multiple solutions for suitable range of λ by analyzing the fibering maps and the corresponding Nehari manifold.

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