Existence of Large Solutions to Semilinear Elliptic Equations with Multiple Terms
Abstract
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).
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 2006
- Accession Number
- ADA455289
Entities
People
- David N. Smith
Organizations
- Air Force Institute of Technology