TY - JOUR

T1 - Sturm theorems and distance between adjacent zeros for second order integro-differential equations

AU - Domoshnitsky, Alexander

N1 - Publisher Copyright:
© 2018 Journal of Nonlinear and Variational Analysis

PY - 2018/8/1

Y1 - 2018/8/1

N2 - Between two adjacent zeros of any nontrivial solution of the second order ordinary differential equation x00(t) + a(t)x0(t) + b(t)x(t) = 0 there is one and only one zero of every nonproportional solution. This principle of zeros’ distribution is known as the Sturm separation theorem which is a basis of many classical results on oscillation and asymptotic properties and on boundary value problems for ordinary differential equations. For delay and integro-differential equations this principle of zeros’ distribution is not true. In this paper, the assertion on validity of the Sturm separation theorem are proposed. Distance between two zeros of nontrivial solutions to integro-differential equations is estimated.

AB - Between two adjacent zeros of any nontrivial solution of the second order ordinary differential equation x00(t) + a(t)x0(t) + b(t)x(t) = 0 there is one and only one zero of every nonproportional solution. This principle of zeros’ distribution is known as the Sturm separation theorem which is a basis of many classical results on oscillation and asymptotic properties and on boundary value problems for ordinary differential equations. For delay and integro-differential equations this principle of zeros’ distribution is not true. In this paper, the assertion on validity of the Sturm separation theorem are proposed. Distance between two zeros of nontrivial solutions to integro-differential equations is estimated.

KW - Boundary value problem

KW - Distance between zeros

KW - Integro-differential equation

KW - Sturm separation theorem

UR - http://www.scopus.com/inward/record.url?scp=85067403265&partnerID=8YFLogxK

U2 - 10.23952/jnva.2.2018.2.04

DO - 10.23952/jnva.2.2018.2.04

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AN - SCOPUS:85067403265

SN - 2560-6921

VL - 2

SP - 155

EP - 164

JO - Journal of Nonlinear and Variational Analysis

JF - Journal of Nonlinear and Variational Analysis

IS - 2

ER -