Year: 2026
Type: article
Abstract: Let f ( t , x ) , M ( t , x ) ∈ C ( [ 0 , 1 ] 2 ) f(t,x),M(t,x)\in C([0,1]^2) with M ( t , x ) > 0 M(t,x)>0 . We consider differential equations of the form \[ ∂ f ∂ t ( t , x ) = M ( t , x ) f ( t , x ) − M ( t , 0 ) f ( t , 0 ) x , x > 0. \frac {\partial f}{\partial t}(t,x)=\frac {M(t,x)f(t,x)-M(t,0)f(t,0)}{x},\quad x>0. \] For a fixed positive weight M M , we ask whether the condition f ( 0 , x ) = 0 f(0,x)=0 forces f ≡ 0 f\equiv 0 . We show the answer is negative for smooth functions: there exist
DOI: 10.1090/proc/17994
Author: Brian Street
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223227757