scholarly journals Sharp Nonexistence Results for a Linear Elliptic Inequality Involving Hardy and Leray Potentials

2011 ◽  
Vol 2011 (1) ◽  
pp. 917201 ◽  
Author(s):  
MouhamedMoustapha Fall ◽  
Roberta Musina
Keyword(s):  
Elliptic Inequality

Oscillation of Semilinear Elliptic Inequalities by Riccati Transformations

1980 ◽  
Vol 32 (4) ◽  
pp. 908-923 ◽  
Author(s):  
E. S. Noussair ◽  
C. A. Swanson
Keyword(s):  
Exterior Domain ◽  
Nonlinear Term ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Second Derivative ◽  
Semilinear Elliptic ◽  
Generalized Riccati Transformation ◽  
The Matrix ◽  
Elliptic Inequality ◽  
Elliptic Inequalities

A generalized Riccati transformation will be utilized to derive a Riccati-type inequality (3) associated with a semilinear elliptic inequality yL(y; x) ≦ 0 possessing a positive solution y in an exterior domain in Euclidean n-space. On the basis of (3), general sufficient conditions for the elliptic inequality to be oscillatory are developed in § 3. The matrix of coefficients of the second derivative terms in L(y;x) (i.e. (Aij) in (1)) is not restricted in any way beyond the usual ellipticity hypothesis (iv) below, and thereby one of the difficulties mentioned in [9] and inherent in the method there is resolved. Furthermore, the nonlinear term B﹛x, y) in (1) is not required to be one-signed.

scholarly journals Quasilinear elliptic inequalities with Hardy potential and nonlocal terms

2020 ◽  
pp. 1-19
Author(s):  
Marius Ghergu ◽  
Paschalis Karageorgis ◽  
Gurpreet Singh
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Hardy Potential ◽  
Existence Of Positive Solutions ◽  
Elliptic Inequality ◽  
Image Position ◽  
Nonlocal Terms ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

We study the quasilinear elliptic inequality \[ -\Delta_m u - \frac{\mu}{|x|^m}u^{m-1} \geq (I_\alpha*u^p)u^q \quad\mbox{in }\mathbb{R}^N\setminus \overline B_1, N\geq 1, \] where $p>0$ , $q, \mu \in \mathbb {R}$ , $m>1$ and $I_\alpha$ is the Riesz potential of order $\alpha \in (0,N)$ . We obtain necessary and sufficient conditions for the existence of positive solutions.

Singular semilinear elliptic inequalities in the exterior of a compact set

2013 ◽  
Vol 143 (3) ◽  
pp. 563-588 ◽  
Author(s):  
Marius Ghergu ◽  
Steven D. Taliaferro
Keyword(s):  
Positive Solutions ◽  
Continuous Functions ◽  
Minimal Solution ◽  
Compact Set ◽  
Optimal Conditions ◽  
Isolated Singularities ◽  
Semilinear Elliptic ◽  
Elliptic Inequality ◽  
Isolated Point ◽  
Elliptic Inequalities

We study the semilinear elliptic inequality –Δu ≥ φ(δK (x))f(u) in ℝN / K, where φ, f are positive and non-increasing continuous functions. Here K ⊂ ℝN (N ≥ 3) is a compact set with finitely many components, each of which is either the closure of a C2 domain or an isolated point, and δK (x) = dist(x, ∂K). We obtain optimal conditions in terms of φ and f for the existence of C2-positive solutions. Under these conditions we prove the existence of a minimal solution and we investigate its behaviour around ∂K as well as the removability of the (possible) isolated singularities.

Nonexistence Results of Positive Entire Solutions for Quasilinear Elliptic Inequalities

1997 ◽  
Vol 40 (2) ◽  
pp. 244-253 ◽  
Author(s):  
Yūki Naito ◽  
Hiroyuki Usami
Keyword(s):  
Sufficient Conditions ◽  
Radial Symmetry ◽  
Entire Solutions ◽  
Elliptic Inequality ◽  
Quasilinear Elliptic ◽  
Elliptic Inequalities

AbstractThis paper treats the quasilinear elliptic inequalitywhere N ≥ 2, m > 1, σ >m− 1, and p:ℝN → (0, ∞) is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When p has radial symmetry, the existence of positive entire solutions can be characterized by our results and some known results.

scholarly journals On Absence of Nonnegative Monotone Solutions for Some Coercive Inequalities in a Half-Space

2017 ◽  
Vol 63 (4) ◽  
pp. 573-585
Author(s):  
E I Galakhov ◽  
O A Salieva
Keyword(s):  
Half Space ◽  
Nonlinear Capacity ◽  
Elliptic Inequality ◽  
Quasilinear Elliptic ◽  
Monotone Solutions ◽  
Capacity Method

Using the nonlinear capacity method, we investigate the problem of absence of nonnegative monotone solutions for a quasilinear elliptic inequality of type Δpu≥uq in a half-space in terms of parameters p and q.

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