Bubbling Solutions for an Anisotropic Emden-Fowler Equation
نویسندگان
چکیده
We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of bubbling solutions. We show that at given local maximum points of a(x), there exists arbitrarily many bubbles. As a consequence, the quantity Tε = ε Z Ω a(x)edx can approach to +∞ as ε → 0. These results show a striking difference with the isotropic case (a(x) ≡ Constant).
منابع مشابه
Analysis of boundary bubbling solutions for an anisotropic Emden-Fowler equation
We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ R is a smooth bounded domain and a is a positive smooth function. We study here the phenomenon of boundary bubbling solutions which do not exist for the isotropic case a ≡ constant. We determine the localization and asymptotic behavior of the boundary bubbles, and construct some bound...
متن کاملApplication of the exact operational matrices for solving the Emden-Fowler equations, arising in Astrophysics
The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the...
متن کاملIntermediate Solutions for Emden–Fowler Type Equations: Continuous Versus Discrete
The existence of a class of nonoscillatory solutions for a generalized Emden–Fowler differential equation is studied. Some analogies and discrepancies between the continuous and discrete case are also discussed. AMS subject classification: Primary 34C10, Secondary 34C15, 39A10.
متن کاملExistence and Uniqueness of Local Weak Solutions for the Emden-fowler Wave Equation in One Dimension
In this article we consider the existence and uniqueness of local weak solutions to the Emden-Fowler type wave equation tutt − uxx = |u|p−1u in [1, T ]× (a, b) with initial-boundary value conditions in a finite time interval.
متن کاملMultiple solutions for boundary value problems of a discrete generalized Emden-Fowler equation
By using critical point theory, some new sufficient conditions for the existence of at least 2N distinct solutions to boundary value problems of a discrete generalized Emden–Fowler equation are obtained. © 2009 Elsevier Ltd. All rights reserved.
متن کامل