Nodal Blow-Up Solutions to Slightly Subcritical Elliptic Problems with Hardy-Critical Term

2017 ◽  
Vol 17 (1) ◽  
Author(s):  
Thomas Bartsch ◽  
Qianqiao Guo
Keyword(s):  
Bounded Domain ◽  
Elliptic Problem ◽  
Blow Up ◽  
Elliptic Problems ◽  
Critical Term

AbstractThe paper is concerned with the slightly subcritical elliptic problem with Hardy-critical termin a bounded domain

Infinitely Many Solutions for Quasilinear Elliptic Problems with Broken Symmetry

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Rossella Bartolo
Keyword(s):  
Bounded Domain ◽  
Elliptic Problem ◽  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Broken Symmetry ◽  
Infinitely Many Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe aim of this paper is investigating the existence of solutions of the quasilinear elliptic Problemwhere Ω is an open bounded domain of R

Blow-up rates of large solutions for a ϕ-Laplacian problem with gradient term

2014 ◽  
Vol 144 (4) ◽  
pp. 669-689 ◽  
Author(s):  
W. Arriagada ◽  
J. Huentutripay
Keyword(s):  
Bounded Domain ◽  
Elliptic Problem ◽  
Blow Up ◽  
Smooth Boundary ◽  
Gradient Term ◽  
Regularly Varying Functions ◽  
Large Solutions ◽  
Regularly Varying ◽  
Increasing Function

We study the behaviour of solutions of a boundary blow-up elliptic problem on a bounded domain Ω with smooth boundary in ℝN. The data of the problem consist of an increasing function f : ℝ+ → ℝ+ and two real regularly varying functions ϕ and g.

Nonlinear elliptic problems on singularly perturbed domains

2001 ◽  
Vol 131 (5) ◽  
pp. 1023-1037 ◽  
Author(s):  
Jaeyoung Byeon
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Singularly Perturbed ◽  
Bounded Domains ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

We consider how the shape of a domain affects the number of positive solutions of a nonlinear elliptic problem. In fact, we show that if a bounded domain Ω is sufficiently close to a union of disjoint bounded domains Ω1,…, Ωm, the number of positive solutions of a nonlinear elliptic problem on Ω is at least 2m −1.

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.

Combined effects in nonlinear singular elliptic problems in a bounded domain

2012 ◽  
Vol 1 (4) ◽  
Author(s):  
Rym Chemmam ◽  
Habib Mâagli ◽  
Syrine Masmoudi ◽  
Malek Zribi
Keyword(s):  
Bounded Domain ◽  
Elliptic Problems ◽  
Combined Effects

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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