Existence of a positive solution for a class of fractional elliptic problems in exterior domains involving critical growth

2021 ◽  
pp. 125543
Author(s):  
Jeziel N. Correia ◽  
Claudionei P. Oliveira
Keyword(s):  
Positive Solution ◽  
Elliptic Problems ◽  
Critical Growth ◽  
Exterior Domains

scholarly journals Localization of solutions for nonlinear elliptic problems with critical growth

2006 ◽  
Vol 343 (11-12) ◽  
pp. 725-730 ◽  
Author(s):  
Rejeb Hadiji ◽  
Riccardo Molle ◽  
Donato Passaseo ◽  
Habib Yazidi
Keyword(s):  
Elliptic Problems ◽  
Critical Growth ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

Decaying Solutions Of 2mth Order Elliptic Problems

1991 ◽  
Vol 43 (3) ◽  
pp. 449-460 ◽  
Author(s):  
W. Allegretto ◽  
L. S. Yu
Keyword(s):  
Positive Solution ◽  
Elliptic Problem ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Weighted Spaces ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Regularity Estimates ◽  
Open Question

AbstractWe consider a semilinear elliptic problem , (n > 2m). Under suitable conditions on f, we show the existence of a decaying positive solution. We do not employ radial arguments. Our main tools are weighted spaces, various applications of the Mountain Pass Theorem and LP regularity estimates of Agmon. We answer an open question of Kusano, Naito and Swanson [Canad. J. Math. 40(1988), 1281-1300] in the superlinear case: , and improve the results of Dalmasso [C. R. Acad. Sci. Paris 308(1989), 411-414] for the case .

scholarly journals Existence and bifurcation for some elliptic problems on exterior strip domains

2006 ◽  
Vol 2006 ◽  
pp. 1-26
Author(s):  
Tsing-San Hsu
Keyword(s):  
Positive Solution ◽  
Elliptic Problem ◽  
Positive Constant ◽  
Elliptic Problems ◽  
Unique Positive Solution ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Strip Domain

We consider the semilinear elliptic problem−Δu+u=λK(x)up+f(x)inΩ,u>0inΩ,u∈H01(Ω), whereλ≥0,N≥3,1<p<(N+2)/(N−2), andΩis an exterior strip domain inℝN. Under some suitable conditions onK(x)andf(x), we show that there exists a positive constantλ∗such that the above semilinear elliptic problem has at least two solutions ifλ∈(0,λ∗), a unique positive solution ifλ=λ∗, and no solution ifλ>λ∗. We also obtain some bifurcation results of the solutions atλ=λ∗.

Positive and nodal solutions for an elliptic equation with critical growth

2016 ◽  
Vol 18 (02) ◽  
pp. 1550021 ◽  
Author(s):  
Marcelo F. Furtado ◽  
Bruno N. Souza
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Critical Growth ◽  
Smooth Domain ◽  
Nodal Solution ◽  
Nodal Solutions ◽  
Bounded Smooth Domain ◽  
Continuous Potential ◽  
Bounded Smooth

We consider the problem [Formula: see text] where [Formula: see text] is a bounded smooth domain, [Formula: see text], [Formula: see text], [Formula: see text]. Under some suitable conditions on the continuous potential [Formula: see text] and on the parameter [Formula: see text], we obtain one nodal solution for [Formula: see text] and one positive solution for [Formula: see text].

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