Existence of Positive Solutions to Weighted Linear Elliptic Equations Under Double Exponential Nonlinearity Growth

2021 ◽  
Author(s):  
Saber Kharrati ◽  
Rached Jaidane
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Exponential Nonlinearity ◽  
Double Exponential ◽  
Existence Of Positive Solutions

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.

On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem

1997 ◽  
Vol 127 (4) ◽  
pp. 691-701 ◽  
Author(s):  
E. N. Dancer ◽  
Juncheng Wei
Keyword(s):  
Boundary Layer ◽  
Dirichlet Problem ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Singularly Perturbed ◽  
Convex Domains ◽  
Existence Of Positive Solutions

We discuss the existence of positive solutions of some singularity perturbed elliptic equations on convex domains with nonlinearity changing sign. In particular, we obtain solutions with both a boundary layer and a sharp interior peak.

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