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. <i>Electronic Journal of Differential Equations, 2017</i>(132), pp. 1-10.
Rights
Attribution 4.0 International