scholarly journals Asymptotic behavior of radial solutions for a semilinear elliptic problem on an annulus through Morse index

2007 ◽  
Vol 239 (1) ◽  
pp. 1-15 ◽  
Author(s):  
P. Esposito ◽  
G. Mancini ◽  
Sanjiban Santra ◽  
P.N. Srikanth
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Problem ◽  
Morse Index ◽  
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.

Morse index and symmetry breaking for an elliptic equation with negative exponent in expanding annuli

2017 ◽  
Vol 147 (6) ◽  
pp. 1215-1232
Author(s):  
Zongming Guo ◽  
Linfeng Mei ◽  
Zhitao Zhang
Keyword(s):  
Elliptic Equation ◽  
Symmetry Breaking ◽  
Morse Index ◽  
Blow Up ◽  
Semilinear Elliptic Equation ◽  
Radial Solutions ◽  
Entire Solutions ◽  
Semilinear Elliptic ◽  
Image Position

Bifurcation of non-radial solutions from radial solutions of a semilinear elliptic equation with negative exponent in expanding annuli of ℝ2 is studied. To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equationThe main results of this paper can be seen as applications of the results obtained recently for finite Morse index solutions of the equationwith N ⩾ 2 and p > 0.

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