Multiple Solutions for a Dirichlet Problem with Jumping Nonlinearities II

No abstract provided for this article

Nonnegative Solutions for a Class of Nonpositone Problems

In the recent past many results have been established on non-negative solutions to boundary value problems of the form -u\u27\u27(x) = λf(u(x)); 0 \u3c x \u3c 1, u(0) = 0 = u(1) where λ\u3e0, f(0)\u3e0 (positone problems). In this paper we consider the impact on the non-negative solutions when f(0)\u3c0. We find that we need f(u) to be convex to guarantee uniqueness of positive solutions, and f(u) to be appropriately concave for multiple positive solutions. This is in contrast to the case of positone problems, where the roles of convexity and concavity were interchanged to obtain similar results. We further establish the existence of non-negative solutions with interior zeros, which did not exist in positone problems

Positive Solutions for a Concave Semipositone Dirichlet Problem

No abstract provided for this articl

Uniqueness of Positive Solutions for a Class of Elliptic Boundary Value Problems

Uniqueness of non-negative solutions conjectured in an earlier paper by Shivaji is proved. Our methods are independent of those of that paper, where the problem was considered only in a ball. Further, our results apply to a wider class of nonlinearities

Nonnegative Solutions to a Semilinear Dirichlet Problem in a Ball Are Positive and Radially Symmetric

We prove that nonnegative solutions to a semilinear Dirichlet problem in a ball are positive, and hence radially symmetric. In particular, this answers a question in [3] where positive solutions were proven to be radially symmetric. In section 4 we provide a sufficient condition on the geometry of the domain which ensures that nonnegative solutions are positive in the interior

Uniqueness of Nonnegative Solutions for Semipositone Problems on Exterior Domains

We consider the problem −Δu = λK(|x|)f(u), x∈Ω u=0 if |x|=r0 u→0 as |x|→∞, where λ is a positive parameter, Δu = div(∇u)is the Laplacian of u, Ω = {x ∈ Rn; n \u3e 2,|x| \u3e r0}, K ∈ C1([r0,∞),(0,∞)) is such that lim r→∞ K(r) = 0 and f ∈ C1([0,∞),R) is a concave function which is sublinear at ∞ and f(0) \u3c 0. We establish the uniqueness of nonnegative radial solutions when λ is large

Positive Solutions for Classes of Multiparameter Elliptic Semipositone Problems

We study positive solutions to multiparameter boundary-value problems of the form -Δu = λg(u)+μf(u) in Ω u = 0 on ∂Ω where λ\u3e0, μ\u3e0, Ω⊆Rn; n≥2 is a smooth bounded domain with ∂Ω in class C2 and Δ is the Laplacian operator. In particular, we assume g(0)\u3e0 and superlinear while f(0