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.

scholarly journals On the Elliptic Problems Involving Multisingular Inverse Square Potentials and Concave-Convex Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Tsing-San Hsu
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Hardy Type ◽  
Multiplicity Of Positive Solutions ◽  
Inverse Square Potentials

A semilinear elliptic problem with concave-convex nonlinearities and multiple Hardy-type terms is considered. By means of a variational method, we establish the existence and multiplicity of positive solutions for problem .

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 Asymptotic Estimates and Qualitative Properties of an Elliptic Problem in Dimension Two

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Khalil El Mehdi ◽  
Massimo Grossi
Keyword(s):  
Bounded Domain ◽  
Elliptic Problem ◽  
Asymptotic Estimates ◽  
Qualitative Properties ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

AbstractIn this paper we study a semilinear elliptic problem on a bounded domain in ℝ

Pointwise Lower Bounds for Solutions of Semilinear Elliptic Equations and Applications

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Asadollah Aghajani ◽  
Alireza Mosleh Tehrani ◽  
Nassif Ghoussoub
Keyword(s):  
Bounded Domain ◽  
Lower Bounds ◽  
Elliptic Problem ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Smooth Bounded Domain ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

AbstractWe consider the semilinear elliptic problem −Δu = f (x, u), posed in a smooth bounded domain Ω of ℝ

On a singular nonlinear semilinear elliptic problem

1998 ◽  
Vol 128 (6) ◽  
pp. 1389-1401 ◽  
Author(s):  
Junping Shi ◽  
Miaoxin Yao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Image Position

We consider the singular boundary value problemWe study the existence, uniqueness, regularity and the dependency on parameters of the positive solutions under various assumptions.

scholarly journals Ground state solutions for a semilinear elliptic problem with critical-subcritical growth

2018 ◽  
Vol 9 (1) ◽  
pp. 108-123 ◽  
Author(s):  
Claudianor O. Alves ◽  
Grey Ercole ◽  
M. Daniel Huamán Bolaños
Keyword(s):  
Continuous Function ◽  
Bounded Domain ◽  
Elliptic Problem ◽  
Ground State ◽  
Ground State Solution ◽  
State Solution ◽  
Subcritical Growth ◽  
Ground State Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

Abstract We prove the existence of at least one ground state solution for the semilinear elliptic problem \left\{\begin{aligned} \displaystyle-\Delta u&\displaystyle=u^{p(x)-1},\quad u% >0,\quad\text{in}\ G\subseteq\mathbb{R}^{N},\ N\geq 3,\\ \displaystyle u&\displaystyle\in D_{0}^{1,2}(G),\end{aligned}\right. where G is either {\mathbb{R}^{N}} or a bounded domain, and {p\colon G\to\mathbb{R}} is a continuous function assuming critical and subcritical values.

Compactly supported solutions for a semilinear elliptic problem in ℝn with sign-changing function and non-Lipschitz nonlinearity

2011 ◽  
Vol 141 (1) ◽  
pp. 127-154 ◽  
Author(s):  
Qiuping Lu
Keyword(s):  
Elliptic Problem ◽  
Mountain Pass Theorem ◽  
Radial Symmetry ◽  
Connected Components ◽  
Compactly Supported ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Lipschitz Nonlinearity ◽  
Image Position ◽  
Compactly Supported Solutions

For a sign-changing function a(x) we consider the solutions of the following semilinear elliptic problem in ℝn with n ≥ 3:where γ > 0 and 0 < q < 1 < p < (n + 2)/(n − 2). Under an appropriate growth assumption on a− at infinity, we show that all solutions are compactly supported. When Ω+ = {x ∈ ℝn | a(x) > 0} has several connected components, we prove that there exists an interval on γ in which the solutions exist. In particular, if a(x) = a(|x|), by applying the mountain-pass theorem there are at least two solutions with radial symmetry that are positive in Ω+.

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