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<p>The aim of this paper is to study the multiplicity of solutions of sixth-order nonlinear differential equations. In particular, by requiring an appropriate behavior on the nonlinearity, we determine an interval of the parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> </InlineEquation> for which the problem admits three solutions. Moreover, we present a result on the existence of three nonnegative solutions, requiring two algebraic sign conditions on the nonlinear term.</p>

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Existence of Three Solutions for a Sixth-Order Nonlinear Differential Equation with Constant Coefficients

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • Lin Li,
  • Shasha Liao,
  • Donal O’Regan

摘要

The aim of this paper is to study the multiplicity of solutions of sixth-order nonlinear differential equations. In particular, by requiring an appropriate behavior on the nonlinearity, we determine an interval of the parameter \(\lambda \) for which the problem admits three solutions. Moreover, we present a result on the existence of three nonnegative solutions, requiring two algebraic sign conditions on the nonlinear term.