scholarly journals Existence and nonexistence results for a weighted elliptic equation in exterior domains

2020 ◽  
Vol 71 (4) ◽  
Author(s):  
Zongming Guo ◽  
Xia Huang ◽  
Dong Ye
Keyword(s):  
Elliptic Equation ◽  
Exterior Domains ◽  
Existence And Nonexistence

Non-homogeneous elliptic equations in exterior domains

2006 ◽  
Vol 136 (1) ◽  
pp. 139-147 ◽  
Author(s):  
J. do Ó ◽  
S. Lorca ◽  
J. Sánchez ◽  
P. Ubilla
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Exterior Domains ◽  
Existence And Multiplicity ◽  
Negative Function ◽  
Multiplicity Of Positive Solutions ◽  
Image Position ◽  
Typical Model ◽  
Homogeneous Elliptic Equation

We study the existence and multiplicity of positive solutions of the non-homogeneous elliptic equation where N ≥ 3, the nonlinearity f is superlinear at both zero and infinity, q is a non-trivial, non-negative function, and a and b are non-negative parameters. A typical model is given by f(u) = up, with p ≥ 1.

Entire Large Solutions to Elliptic Equations of Power Non-linearities with Variable Exponents

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Alan V. Lair ◽  
Ahmed Mohammed
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Variable Exponents ◽  
Large Solutions ◽  
Existence And Nonexistence

AbstractWe give conditions on the variable exponent q that ensure the existence and nonexistence of a positive solution to the elliptic equation Δu = u

scholarly journals A nonexistence result for a nonlinear elliptic equation with singular and decaying potential

2015 ◽  
Vol 17 (04) ◽  
pp. 1450024 ◽  
Author(s):  
Marino Badiale ◽  
Michela Guida ◽  
Sergio Rolando
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Nonlinear Elliptic Equation ◽  
Negative Answer ◽  
Radial Solutions ◽  
Compatibility Conditions ◽  
Nonlinear Elliptic ◽  
Nonexistence Result ◽  
Open Case ◽  
Existence And Nonexistence

Several existence and nonexistence results are known for positive solutions u ∈ D1,2(ℝN) ∩ L2(ℝN, ∣x∣-αdx) ∩ Lp(ℝN) to the equation [Formula: see text] resting upon compatibility conditions between α and p. Letting 2α := 2N/(N - α) and [Formula: see text], the problem is still open for 0 < α < 2 and [Formula: see text], for 2 < α < N and [Formula: see text], and for N ≤ α < 2N - 2 and [Formula: see text]. Here we give a negative answer to the problem of the existence of radial solutions in the first open case.

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