Existence and nonexistence of solutions for sublinear problems with prescribed number of zeros on exterior domains
Date
2017-05-16
Authors
Joshi, Janak
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We prove existence of radial solutions of ∆u + K(r)ƒ(u) = 0 on the exterior of the ball, of radius R, centered at the origin in ℝN such that lim r→∞ u(r) = 0 if R > 0 is sufficiently small. We assume ƒ : ℝ → ℝ is odd and there exists a β > 0 with ƒ < 0 on (0, β), ƒ > 0 on (β, ∞) with ƒ sublinear for large u, and K(r) ~ r-α for large r with α > 2(N - 1). We also prove nonexistence if R > 0 is sufficiently large.
Description
Keywords
Exterior domain, Sublinear, Radial solution
Citation
Joshi, J. (2017). Existence and nonexistence of solutions for sublinear problems with prescribed number of zeros on exterior domains. Electronic Journal of Differential Equations, 2017(132), pp. 1-10.
Rights
Attribution 4.0 International