Decaying positive solutions to a system of nonlinear elliptic equations

In this paper, the second-order nonlinear elliptic system with α, γ < 1 and β ≥ 1, is considered in RN, N ≥ 3. Under suitable hypotheses on functions fi, gi, hi (i = 1, 2) and P, it is shown that this system possesses an entire positive solution , 0 < θ < 1, such that both u and v are bounded below and above by constant multiples of |x|2−N for all |x| ≥ 1.

Download Full-text

Solutions with multiple peaks for nonlinear elliptic equations

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050002134x ◽

1999 ◽

Vol 129 (2) ◽

pp. 235-264 ◽

Cited By ~ 31

Author(s):

Daomin Cao ◽

Ezzat S. Noussair ◽

Shusen Yan

Keyword(s):

Positive Solutions ◽

Critical Points ◽

Elliptic Equations ◽

Nonlinear Elliptic Equations ◽

Multiple Peaks ◽

Nonlinear Elliptic ◽

Image Position

Solutions with peaks near the critical points of Q(x) are constructed for the problemWe establish the existence of 2k −1 positive solutions when Q(x) has k non-degenerate critical points in ℝN

Download Full-text

Asymptotic behaviour and symmetry of positive solutions to nonlinear elliptic equations in a half-space

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210515000876 ◽

2016 ◽

Vol 146 (6) ◽

pp. 1243-1263 ◽

Cited By ~ 3

Author(s):

Lei Wei

Keyword(s):

Half Space ◽

Positive Solutions ◽

Elliptic Equations ◽

Nonlinear Elliptic Equations ◽

Unique Positive Solution ◽

Bounded Smooth Domain ◽

Nonlinear Elliptic ◽

Bounded Smooth ◽

Image Position ◽

General Nonlinearity

We consider the following equation:where d(x) = d(x, ∂Ω), θ > –2 and Ω is a half-space. The existence and non-existence of several kinds of positive solutions to this equation when , f(u) = up(p > 1) and Ω is a bounded smooth domain were studied by Bandle, Moroz and Reichel in 2008. Here, we study exact the behaviour of positive solutions to this equation as d(x) → 0+ and d(x) → ∞, respectively, and the symmetry of positive solutions when , Ω is a half-space and f(u) is a more general nonlinearity term than up. Under suitable conditions for f, we show that the equation has a unique positive solution W, which is a function of x1 only, and W satisfies

Download Full-text

Symmetry and Nonexistence of Positive Solutions for a Fractional Laplacion System with Coupled Terms

10.21203/rs.3.rs-1024420/v1 ◽

2022 ◽

Author(s):

Rong Zhang

Keyword(s):

Positive Solution ◽

Elliptic System ◽

Bounded Domain ◽

Positive Solutions ◽

Critical Case ◽

Nonlinear Elliptic System ◽

Subcritical Case ◽

Nonlinear Elliptic ◽

Method Of Moving Planes ◽

Moving Planes

Abstract In this paper, we study the problem for a nonlinear elliptic system involving fractional Laplacion: (equation 1.1) where 0 < α, β < 2, p, q > 0 and max{p, q} ≥ 1, α + γ > 0, β + τ > 0, n ≥ 2. First of all, while in the subcritical case, i.e. n + α + γ − p(n − α) − (q + 1)(n − β) > 0, n + β + τ − (p + 1)(n − α) − q(n − β) > 0, we prove the nonexistence of positive solution for the above system in R n . Moreover, though Doubling Lemma to obtain the singularity estimates of the positive solution on bounded domain Ω. In addition, while in the critical case, i.e. n+α+γ −p(n−α)−(q + 1)(n−β) = 0, n+β +τ −(p+ 1)(n−α)−q(n−β) = 0, we show that the positive solution of above system are radical symmetric and decreasing about some point by using the method of Moving planes in Rn Mathematics Subject Classification (2020): 35R11, 35A10, 35B06.

Download Full-text

Uniqueness of positive solutions of nonlinear elliptic equations with exponential growth

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500003012 ◽

2003 ◽

Vol 133 (6) ◽

pp. 1409-1420 ◽

Cited By ~ 3

Author(s):

Cristina Tarsi

Keyword(s):

Positive Solutions ◽

Exponential Growth ◽

Elliptic Equations ◽

Nonlinear Elliptic Equations ◽

Inversion Technique ◽

Nonlinear Elliptic ◽

Image Position

By combining a technique inspired to the theory of sublinear elliptic equations with the Emden-Fowler inversion technique of Atkinson and Peletier, we obtain uniqueness of positive solutions of the following equation where B ⊂ Rn is the ball of radius one, λ > 0 and 1 < ϑ ≤ 2.

Download Full-text

A CRITERION FOR EXISTENCE OF A POSITIVE SOLUTION OF A NONLINEAR ELLIPTIC SYSTEM

Analysis and Applications ◽

10.1142/s0219530508001171 ◽

2008 ◽

Vol 06 (03) ◽

pp. 299-321 ◽

Cited By ~ 2

Author(s):

J. VELIN

Keyword(s):

Positive Solution ◽

Elliptic System ◽

Positive Solutions ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Nonlinear Elliptic System ◽

Nonlinear Elliptic ◽

Potential Type ◽

Necessary And Sufficient

In this paper, we give necessary and sufficient conditions for existence of bounded and positive solutions of a nonlinear elliptic system arising from potential type problems.

Download Full-text