We consider a second-order differential equation with rapidly growing intermediate coefficients. We obtain a solvability result in the cases that the diffusion coefficient of equation is unbounded or it tends to zero at the infinity. Under additional conditions, we prove the $L_p - $ maximal regularity estimate for the solution of this equation.
Second-order differential equation, unbounded intermediate coefficient, existence of a solution, uniqueness, maximal regularity estimate
OSPANOV, KORDAN and YESBAYEV, ADILET
"Solvability and maximal regularity results for a differential equation with diffusion coefficient,"
Turkish Journal of Mathematics: Vol. 44:
4, Article 16.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss4/16