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Uniqueness result and iterative method for fourth order $p$-Laplacian integral boundary value problems with different nonlinear terms
  • Youyuan Yang,
  • jianfeng huang,
  • Liguo Yuan
Youyuan Yang
Guangdong University of Finance

Corresponding Author:[email protected]

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jianfeng huang
Guangdong University of Finance
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Liguo Yuan
South China Agricultural University
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In this paper, by using the contraction mapping principle, we establish the existence and uniqueness of solutions for the fourth order $p$-Laplacian beam equations $(\Phi_{p}(u’‘(t)))’‘=f(t, u(t), u’(t), u’‘(t))$ with integral boundary conditions $u’‘(0)=u’‘(1)=0,u(0)-\alpha u’(0)= \int_{0}^{1}g_{1}(s)u(s)ds, u(1)+\beta u’(1)= \int_{0}^{1}g_{2}(s)u(s)ds$. The monotony of iterations is also considered. As an extension, we obtain the uniqueness and iterative solutions of the fourth order $p$-Laplacian integral boundary value problems with fully nonlinear term $(\Phi_{p}(u’‘(t)))’‘=f(t, u(t), u’(t), u’‘(t), u”’(t))$. At last, some examples are presented to illustrate the main results.