Existence of solutions for sublinear equations on exterior domains
Texas State University, Department of Mathematics
In this article we prove the existence of an infinite number of radial solutions of ∆u + K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝN with u = 0 on ∂BR and lim r→∞ u(r) = 0 where N > 2, ƒ is odd with ƒ < 0 on (0, β), ƒ > 0 on (β, ∞), ƒ(u) ~ up with 0 < p < 1 for large u and K(r) ~ r-α with 0 < α < 2 for large r.
Exterior domains, Semilinear, Sublinear, Radial
Iaia, J. A. (2017). Existence of solutions for sublinear equations on exterior domains. <i>Electronic Journal of Differential Equations, 2017</i>(253), pp. 1-14.