Existence of Large Solutions to Semilinear Elliptic Equations with Multiple Terms

摘要

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.