Existence of nonnegative solutions to superlinear second order problems of 
the form <mml:math alttext="$y'' + \mu q\left( t \right)g\left( {t,y} \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>y</mml:mi><mml:mo>&#8243;</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mi>&#956;</mml:mi><mml:mi>q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> is discussed in this paper. Here <mml:math alttext="$\mu  \geqslant 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#956;</mml:mi><mml:mo>&#8805;</mml:mo><mml:mn>0</mml:mn></mml:math> is a parameter.

International Journal of Stochastic Analysis

Nonnegative solutions to superlinear problems of generalized Gelfand type

Abstract

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