Correct solvability of the Sturm-Liouville equation with delayed argument

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• 作者：N.A. Chernyavskaya^a ; ^{nina@math.bgu.ac.il" class="auth_mail" title="E-mail the corresponding author} ; L.A. Shuster^b ; ^{miriam@macs.biu.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34B05 ; 34B24 ; 34K06
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：261
• 期：6
• 页码：3247-3267
• 全文大小：319 K

文摘

We consider the equation where f∈C(R)$f\in C(\mathbb{R})$ and Here C^loc(R)$C^{\mathrm{loc}}(\mathbb{R})$ is the set of functions continuous in every point of the number axis. By a solution of (1), we mean any function y  , doubly continuously differentiable everywhere in ac0cebcb5381d0df6e3107fcb" title="Click to view the MathML source">R$\mathbb{R}$, which satisfies (1). We show that under certain additional conditions on the functions φ and q to (2), (1) has a unique solution y, satisfying the inequality where the constant c∈(0,∞)$c\in (0,\infty )$ does not depend on the choice of f∈C(R)$f\in C(\mathbb{R})$.