The aim of the paper is to give an oscillation theorem for inhomogeneous Stieltjes integro-differential equation of the form <mml:math alttext="$p\left( t \right)x' + \int\limits_a^t {x\left( s \right)} d\sigma  = f\left( t \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mo>&#8242;</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:munderover><mml:mo>&#8747;</mml:mo><mml:mi>a</mml:mi><mml:mi>t</mml:mi></mml:munderover><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mi>d</mml:mi><mml:mi>&#963;</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>. The paper generalizes the author&#39;s work [2].

International Journal of Mathematics and Mathematical Sciences

An oscillation criterion for inhomogeneous Stieltjes integro-differential equations

Abstract

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