TITLE

Isolated boundary singularities of semilinear elliptic equations

AUTHOR(S)
Bidaut-Véron, Marie-Françoise; Ponce, Augusto; Véron, Laurent
PUB. DATE
January 2011
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2011, Vol. 40 Issue 1/2, p183
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Given a smooth domain $${\Omega\subset\mathbb{R}^N}$$ such that $${0 \in \partial\Omega}$$ and given a nonnegative smooth function ζ on ∂Ω, we study the behavior near 0 of positive solutions of −Δ u = u in Ω such that u = ζ on ∂Ω\{0}. We prove that if $${\frac{N+1}{N-1} < q < \frac{N+2}{N-2}}$$ , then $${u(x)\leq C |x|^{-\frac{2}{q-1}}}$$ and we compute the limit of $${|x|^{\frac{2}{q-1}} u(x)}$$ as x → 0. We also investigate the case $${q= \frac{N+1}{N-1}}$$ . The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains.
ACCESSION #
55471513

 

Related Articles

  • Radially Symmetric Solutions of Δw + ∣w∣p-1w = 0. Troy, William C.; Krisner, Edward P. // International Journal of Differential Equations;2012, p1 

    We investigate solutions of w" + ((N - 1)/r)w' + ∣w∣p-1w = 0, r > 0 and focus on the regime N > 2 and p > N/(N - 2). Our advance is to develop a technique to efficiently classify the behavior of solutions on (rmin, rmax), their maximal positive interval of existence. Our approach is to...

  • An existence principle for solutions to a singular boundary-value problems. Weng, Shiyou; Gao, Haiyin; Jiang, Daqing; Hou, Xuezhang // Journal of Mathematical Sciences;Sep2011, Vol. 177 Issue 3, p466 

    The singular boundary-value problemis studied. The singularity may appear at u = 0, and the function g may change sign. An existence theorem for solutions to the above boundary-value problem is proposed, and it is proved via the method of upper and lower solutions.

  • Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space. Bo Liu; Yansheng Liu // Journal of Function Spaces & Applications;2013, p1 

    This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient...

  • Positive Solutions for Systems of Singular Higher-Order Multi-Point Boundary Value Problems. Henderson, Johnny; Luca, Rodica // British Journal of Mathematics & Computer Science;2014, Vol. 4 Issue 4, p460 

    We study the existence of positive solutions of a system of higher-order nonlinear differential equations subject to multi-point boundary conditions, where the nonlinearities do not possess any sublinear or superlinear growth conditions and may be singular. In the proof of the main results, we...

  • Nonlinear elliptic problems with a singular weight on the boundary. Dávila, Juan; Peral, Ireneo // Calculus of Variations & Partial Differential Equations;Jul2011, Vol. 41 Issue 3/4, p567 

    We study existence of solutions to with u = 0 on ∂Ω, where Ω is a smooth bounded domain in $${\mathbb {R}^N}$$ , N ≥ 3 with $${0\,\in\,\partial \Omega}$$ and $${1< p < \frac{N+2}{N-2}}$$ . The existence of solutions depends on the geometry of the domain. On one hand, if the...

  • MULTIPLE SOLUTIONS FOR NONRESONANCE IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS. Benchohra, Mouffak; Ouahab, Abdelghani // Electronic Journal of Differential Equations;2003, Vol. 2003, p1 

    In this paper we investigate the existence of multiple solutions for first and second order impulsive functional differential equations with boundary conditions. Our main tool is the Leggett and Williams fixed point theorem.

  • Existence of solutions for a class of fourth-order m-point boundary value problems. Jian-Ping Sun; Qiu-Yan Ren // Electronic Journal of Qualitative Theory of Differential Equatio;Mar2010, Special section p1 

    Some existence criteria are established for a class of fourth-order m-point boundary value problem by using the upper and lower solution method and the Leray-Schauder continuation principle.

  • Positive Solutions to Periodic Boundary Value Problems for Four-Order Differential Equations. Huantao Zhu; Zhiguo Luo // ISRN Mathematical Analysis;2012, p1 

    We apply fixed point theorem in a cone to obtain sufficient conditions for the existence of single and multiple positive solutions of periodic boundary value problems for a class of four-order differential equations.

  • Mixed problems for the Lavrent'ev-Bitsadze equation. Soldatov, Alexander P. // AIP Conference Proceedings;Nov2012, Vol. 1497 Issue 1, p199 

    For Lavrentiev -Bitsadze equation we consider boundary value problems with Dirichlet dates on part or whole boundary of mixed domain. We formulate results results on existence and uniqueness of solution for these problems in scale of Holder weighted classes.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics