Green-Liouville approximation and correct solvability in $L_p(\mathbb R)$ of the general Sturm-Liouville equation

Chernyavskaya, Nina ; Shuster, Leonid

Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 247-272

Abstract (VO)

We consider the equation $$ -(r(x) y'(x))'+q(x)y(x)=f(x),\quad x\in \mathbb R, $$ where $f\in L_p(\mathbb R)$, $p\in (1,\infty )$ and $$ r>0,\quad \frac {1}{r}\in L_1^{\rm loc}(\mathbb R),\quad q\in L_1^{\rm loc}(\mathbb R). $$ For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions $r$ and $q$ under which the above equation is correctly solvable in the space $L_p(\mathbb R),$ $p\in (1,\infty ).$

Détail

DOI : 10.21136/CMJ.2024.0175-23

Classification : 34B24, 34B27
Keywords: Green-Liouville approximation; correct solvability; general Sturm-Liouville equation

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