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Youfeng Zhang,Zhiyu Zhang,Fengqin Zhang 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we consider themultipoint boundary value prob- lem for the one-dimensional p-Laplacian (∅p(u'))'(t) + q(t)f(t,u(t), u'(t)) = 0, t ∈ (0, 1), subject to the boundary conditions: u(0) =<수식> , u(1) =<수식> where ∅p(s) = |s|n−2s, p > 1, ξi ∈ (0, 1) with 0 < ξ1 < ξ2 < · · · < ξn−2 < 1 and αi, βi ∈ [0, 1), 0 < <수식> ,<수식> βi < 1. Using a fixed point theoremdue to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative. In this paper, we consider themultipoint boundary value prob- lem for the one-dimensional p-Laplacian (∅p(u'))'(t) + q(t)f(t,u(t), u'(t)) = 0, t ∈ (0, 1), subject to the boundary conditions: u(0) =<수식> , u(1) =<수식> where ∅p(s) = |s|n−2s, p > 1, ξi ∈ (0, 1) with 0 < ξ1 < ξ2 < · · · < ξn−2 < 1 and αi, βi ∈ [0, 1), 0 < <수식> ,<수식> βi < 1. Using a fixed point theoremdue to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.
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Zhang, Youfeng,Zhang, Zhiyu,Zhang, Fengqin The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.
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