scholarly journals On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^n$

2005 ◽  
Vol 4 (1) ◽  
pp. 187-198 ◽  
Author(s):  
Haitao Yang ◽  
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Problem ◽  
Large Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

scholarly journals Radial symmetry of large solutions of semilinear elliptic equations with convection

2014 ◽  
Vol 144 (1) ◽  
pp. 139-147
Author(s):  
Ehsan Kamalinejad ◽  
Amir Moradifam
Keyword(s):  
Elliptic Problem ◽  
Elliptic Equations ◽  
Radial Solution ◽  
Radial Symmetry ◽  
Semilinear Elliptic Equations ◽  
Rate Of Growth ◽  
Large Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

We study the radial symmetry of large solutions of the semilinear elliptic problem Δu + ∇h · ∇u = f (∣x∣, u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of growth of the solution at infinity.

NONNEGATIVE SOLUTIONS FOR INDEFINITE SUBLINEAR ELLIPTIC PROBLEMS

2012 ◽  
Vol 14 (03) ◽  
pp. 1250021 ◽  
Author(s):  
FRANCISCO ODAIR DE PAIVA
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Solution Method ◽  
Mountain Pass Theorem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Nonnegative Solutions ◽  
Carathéodory Function ◽  
Multiplicity Of Positive Solutions

This paper is devoted to the study of existence, nonexistence and multiplicity of positive solutions for the semilinear elliptic problem [Formula: see text] where Ω is a bounded domain of ℝN, λ ∈ ℝ and g(x, u) is a Carathéodory function. The obtained results apply to the following classes of nonlinearities: a(x)uq + b(x)up and c(x)(1 + u)p (0 ≤ q < 1 < p). The proofs rely on the sub-super solution method and the mountain pass theorem.

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 .

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