Scholarlink

<p>This paper investigates a class of fourth-order beam equations with <i>p</i>-th growth terms under Riemann–Stieltjes integral boundary conditions. The related fixed-point operators are derived using the variation of parameters method. We establish an integral expression for the estimate of the norm of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(u'''\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>u</mi> <mrow> <mo>′</mo> <mo>′</mo> <mo>′</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> using the Gronwall-type inequality. We employ the integrating factor methods to derive an estimate for the norm of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(u'''\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>u</mi> <mrow> <mo>′</mo> <mo>′</mo> <mo>′</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>, which must satisfy a boundary condition without an analytical solution. By applying scaling technique, we simplify the aforementioned boundary conditions and obtain a priori bound for the norm of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(u'''\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>u</mi> <mrow> <mo>′</mo> <mo>′</mo> <mo>′</mo> </mrow> </msup> </math></EquationSource> </InlineEquation>. The existence and multiplicity of positive solutions for the boundary value problem are proven by leveraging the properties of the fixed-point index. We provide two examples to validate the theoretical results. Finally, we summarize the main results of this paper.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Multiple positive solutions of fourth-order beam equations with p-th growth terms under Riemann–Stieltjes integral boundary conditions

  • 期刊论文

  • 发表日期：

    2026年2月16日

查看全文
  • Youyuan Yang,
  • Shaoyan Zhang,
  • Qiru Wang

摘要

This paper investigates a class of fourth-order beam equations with p-th growth terms under Riemann–Stieltjes integral boundary conditions. The related fixed-point operators are derived using the variation of parameters method. We establish an integral expression for the estimate of the norm of \(u'''\) u ′ ′ ′ using the Gronwall-type inequality. We employ the integrating factor methods to derive an estimate for the norm of \(u'''\) u ′ ′ ′ , which must satisfy a boundary condition without an analytical solution. By applying scaling technique, we simplify the aforementioned boundary conditions and obtain a priori bound for the norm of \(u'''\) u ′ ′ ′ . The existence and multiplicity of positive solutions for the boundary value problem are proven by leveraging the properties of the fixed-point index. We provide two examples to validate the theoretical results. Finally, we summarize the main results of this paper.