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<p>We present results concerning value distribution of solutions of two second order equations with transcendental coefficients. The equations are related to Painlevé equations <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P_3\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(P_5\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mn>5</mn> </msub> </math></EquationSource> </InlineEquation>, but also interrelated with each other. We mainly focus on the existence of exceptional values, but consider other value distribution and growth properties of their solutions.</p>

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On Some Second Order Equations Associated with Painlevé Third and Fifth Equation

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Ewa Ciechanowicz

摘要

We present results concerning value distribution of solutions of two second order equations with transcendental coefficients. The equations are related to Painlevé equations \(P_3\) P 3 and \(P_5\) P 5 , but also interrelated with each other. We mainly focus on the existence of exceptional values, but consider other value distribution and growth properties of their solutions.