TY - JOUR
T1 - Nonexistence of radial time-periodic solutions of reaction-diffusion equations with generic nonlinearities
AU - Poláčik, Peter
N1 - Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2023/8/5
Y1 - 2023/8/5
N2 - We consider reaction-diffusion equations ut=Δu+f(u) on the entire space RN, N≥4. Assuming that the function f is sufficiently smooth (C2 is sufficient) and has only nondegenerate zeros, we prove that the equation has no bounded solutions u(x,t) which are radial in x, and periodic and nonconstant in t. We also prove some weaker nonexistence results for N=3. In dimensions N=1,2, the nonexistence of time-periodic solutions (radial or not) is known by results of Gallay and Slijepčević.
AB - We consider reaction-diffusion equations ut=Δu+f(u) on the entire space RN, N≥4. Assuming that the function f is sufficiently smooth (C2 is sufficient) and has only nondegenerate zeros, we prove that the equation has no bounded solutions u(x,t) which are radial in x, and periodic and nonconstant in t. We also prove some weaker nonexistence results for N=3. In dimensions N=1,2, the nonexistence of time-periodic solutions (radial or not) is known by results of Gallay and Slijepčević.
KW - Periodic solutions
KW - Reaction-diffusion equations on the entire space
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U2 - 10.1016/j.jde.2023.03.018
DO - 10.1016/j.jde.2023.03.018
M3 - Article
AN - SCOPUS:85150413951
SN - 0022-0396
VL - 363
SP - 307
EP - 326
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -