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Existence Of Large Solutions To Semilinear Elliptic Equations With Multiple Terms, David N. Smith
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
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 g1 ≤ f ≤ 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) …