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2006

Physical Sciences and Mathematics

Theses and Dissertations

Differential equations

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Existence Of Large Solutions To Semilinear Elliptic Equations With Multiple Terms, David N. Smith Sep 2006

Existence Of Large Solutions To Semilinear Elliptic Equations With Multiple Terms, David N. Smith

Theses and Dissertations

We consider the semilinear elliptic equation Δu = p(x)uα + q(x)uβ on a domain Ω ⊆ Rn, n ≥ 3, where p and q are nonnegative continuous functions with the property that each of their zeroes is contained in a bounded domain Ωp or Ωq, respectively in Ω such that p is positive on the boundary of Ωp and q is positive on the boundary of Ωq. For Ω bounded, we show that there exists a nonnegative solution u such that u(x) → ∞ as x → ∂Ω if …


Existence Of Explosive Solutions To Non-Monotone Semilinear Elliptic Equations, Zachary H. Proano Mar 2006

Existence Of Explosive Solutions To Non-Monotone Semilinear Elliptic Equations, Zachary H. Proano

Theses and Dissertations

We consider the semilinear elliptic equation Δu = p(x)f(u) on a domain ­ Ω ⊆ Rn, n ≥ 3, where f is a nonnegative function which vanishes at the origin and satisfies g1f g2 where g1; g2 are nonnegative, nondecreasing functions which also vanish at the origin, and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in ­ such that p is positive on its boundary. For Ω­ bounded, we show that a nonnegative solution u satisfying u(x) …