Solutions with multiple peaks for nonlinear elliptic equations

1999 ◽  
Vol 129 (2) ◽  
pp. 235-264 ◽  
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

Decaying positive solutions to a system of nonlinear elliptic equations

2006 ◽  
Vol 136 (2) ◽  
pp. 301-320
Author(s):  
Fenfei Chen ◽  
Miaoxin Yao
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Second Order ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Bounded Below

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.

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

2016 ◽  
Vol 146 (6) ◽  
pp. 1243-1263 ◽  
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

Uniqueness of positive solutions of nonlinear elliptic equations with exponential growth

2003 ◽  
Vol 133 (6) ◽  
pp. 1409-1420 ◽  
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.

On some nonlinear elliptic equations involving derivatives of the nonlinearity

1985 ◽  
Vol 100 (3-4) ◽  
pp. 281-294 ◽  
Author(s):  
J. Carrillo ◽  
M. Chipot
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Elliptic Boundary ◽  
Nonlinear Elliptic Equations ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Derivatives Of

SynopsisWe give some results on existence and uniqueness for the solution of elliptic boundary value problems of typewhen the βi are not necessarily smooth.

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