Asymptotic decay of oscillatory solutions of second order differential equations with forcing term
Asymptotic decay of oscillatory solutions of second order differential equations with forcing term
The ordinary differential equation<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis p left-parenthesis t right-parenthesis y prime right-parenthesis prime plus q left-parenthesis t right-parenthesis f left-parenthesis y right-parenthesis equals r left-parenthesis t right-parenthesis"><mml:semantics><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>′</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>r</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">(p(t)y’)’ + q(t)f(y) = r(t)</mml:annotation></mml:semantics></mml:math></inline-formula>and its companion functional differential equation are …