DTIC ADA455289: Existence of Large Solutions to pdf

DTIC ADA455289: Existence of Large Solutions to

More Book Details

Description of the Book:

We consider the semilinear elliptic equation Delta u = p(x)u(sup alpha) + q(x)u(sup beta) on a domain Omega reflex subset contained in real number(sup n), n or = 3, where p and q are nonnegative continuous functions with the property that each of their zeroes is contained in a bounded domain Omega(sub p) or Omega(sub q), respectively in Omega such that p is positive on the boundary of Omega(sub p) and q is positive on the boundary of Omega(sub q). For Omega bounded, we show that there exists a nonnegative solution u such that u(x) towards infinity as x towards the derivative of Omega is 0 is alpha is or = to beta, and beta is 1, and that such a solution does not exist is 0 is alpha is or = beta is or = to 1. For Omega = real number(sup n), we established conditions on p and q to guarantee the existence of a nonnegative solution u satisfying u(x) towards infinity as the absolute value of x approaches infinity for 0 alpha is or = beta, and beta 1, and for 0 alpha is or = beta is or = 1.

For Omega=real number(sup n) and 0 , alpha and = beta and 1, we also establish conditions on p and q for the existence and nonexistence of a solution of u where u is bounded on Real number(sup n

• Creator/s: Defense Technical Information Center
• Date: 9/1/2006
• Year: 2006
• Book Topics/Themes: DTIC Archive, Smith, David N, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING AND MANAGEMENT, *SOLUTIONS(GENERAL), *PARTIAL DIFFERENTIAL EQUATIONS, THESES, MATHEMATICAL ANALYSIS

An excerpt captured from the PDF book