TY - JOUR

T1 - Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition

AU - Fila, Marek

AU - Ishige, Kazuhiro

AU - Kawakami, Tatsuki

PY - 2015/10/22

Y1 - 2015/10/22

N2 - We consider the semilinear elliptic equation – Δu = up, p > 1, u = u (x,t) x ∈ ℝN+, t > 0, with a dynamical boundary condition. We show that, for p < (N+1)/(N-1), there exist no nontrivial nonnegative local-in-time solutions. Furthermore, in the case P > (N+1)/(N-1)$$p>(N+1)/(N-1), we determine the optimal slow decay rate at spatial infinity for initial data giving rise to global bounded positive solutions.

AB - We consider the semilinear elliptic equation – Δu = up, p > 1, u = u (x,t) x ∈ ℝN+, t > 0, with a dynamical boundary condition. We show that, for p < (N+1)/(N-1), there exist no nontrivial nonnegative local-in-time solutions. Furthermore, in the case P > (N+1)/(N-1)$$p>(N+1)/(N-1), we determine the optimal slow decay rate at spatial infinity for initial data giving rise to global bounded positive solutions.

KW - 35B40

KW - 35J25

KW - 35J91

UR - http://www.scopus.com/inward/record.url?scp=84941993385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941993385&partnerID=8YFLogxK

U2 - 10.1007/s00526-015-0856-8

DO - 10.1007/s00526-015-0856-8

M3 - Article

AN - SCOPUS:84941993385

VL - 54

SP - 2059

EP - 2078

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 2

ER -