Infinitely many radial solutions of a semilinear elliptic problem on ?N

1993 ◽  
Vol 124 (3) ◽  
pp. 261-276 ◽  
Author(s):  
Thomas Bartsch ◽  
Michel Willem
Keyword(s):  
Elliptic Problem ◽  
Radial Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

scholarly journals Radial solutions of a semilinear elliptic problem

1991 ◽  
Vol 118 (3-4) ◽  
pp. 305-326
Author(s):  
M. A. Herrero ◽  
J. J. L. Velázquez
Keyword(s):  
Asymptotic Behaviour ◽  
Elliptic Problem ◽  
Nonnegative Function ◽  
Radial Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Almost Everywhere ◽  
Image Position

SynopsisWe analyse the set of nonnegative, global, and radial solutions (radial solutions, for short) of the equationwhere 0 < p < 1, and is a radial and almost everywhere nonnegative function. We show that radial solutions of (E) exist if f(r) = o(r2p/1−1−p) or if f(r) ≈ cr2p/1−p as r → ∞, whereWhen f(r) = c*r2p/1−p + h(r) with h(r) = o(r2p/1−p) as r → ∞, radial solutions continue to exist if h(r) is sufficiently small at infinity. Existence, however, breaks down if h(r) > 0,Whenever they exist, radial solutions are characterised in terms of their asymptotic behaviour as r → ∞.

Multiplicity of non-radial solutions of critical elliptic problems in an annulus

2005 ◽  
Vol 135 (1) ◽  
pp. 25-37 ◽  
Author(s):  
Djairo Guedes de Figueiredo ◽  
Olímpio Hiroshi Miyagaki
Keyword(s):  
Critical Points ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Critical Sobolev Exponent ◽  
Radial Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Sobolev Exponent ◽  
Image Position

By looking for critical points of functionals defined in some subspaces of , invariant under some subgroups of O (N), we prove the existence of many positive non-radial solutions for the following semilinear elliptic problem involving critical Sobolev exponent on an annulus, where 2* − 1 := (N + 2)/(N − 2) (N ≥ 4), the domain is an annulus and f : R+ × R+ → R is a C1 function, which is a subcritical perturbation.

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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