Geodesic
Existence of multiple positive solutions of $n{\rm th}$-order $m$-point boundary value problems
Mathematica Bohemica, Tome 135 (2010) no. 1, pp. 15-28

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The paper deals with the existence of multiple positive solutions for the boundary value problem $$ \begin{cases} (\varphi (p(t)u^{(n-1)})(t))' + a(t)f(t, u(t), u'(t), \ldots , u^{(n-2)}(t)) = 0, \quad \ 0 t 1, \\ u^{(i)}(0) = 0, \quad i = 0, 1, \ldots , n - 3,\\ u^{(n-2)}(0) = \sum _{i=1}^{m-2}\alpha _iu^{(n-2)}(\xi _i),\quad u^{(n-1)}(1) = 0, \end{cases} $$ where $\varphi \colon \Bbb R \rightarrow \Bbb R$ is an increasing homeomorphism and a positive homomorphism with $\varphi (0) = 0$. Using a fixed-point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.
The paper deals with the existence of multiple positive solutions for the boundary value problem $$ \begin{cases} (\varphi (p(t)u^{(n-1)})(t))' + a(t)f(t, u(t), u'(t), \ldots , u^{(n-2)}(t)) = 0, \quad \ 0 t 1, \\ u^{(i)}(0) = 0, \quad i = 0, 1, \ldots , n - 3,\\ u^{(n-2)}(0) = \sum _{i=1}^{m-2}\alpha _iu^{(n-2)}(\xi _i),\quad u^{(n-1)}(1) = 0, \end{cases} $$ where $\varphi \colon \Bbb R \rightarrow \Bbb R$ is an increasing homeomorphism and a positive homomorphism with $\varphi (0) = 0$. Using a fixed-point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.
DOI : 10.21136/MB.2010.140679
Classification : 34B18
Keywords: boundary-value problems; positive solutions; fixed-point theorem; cone 
Liang, Sihua; Zhang, Jihui. Existence of multiple positive solutions of $n{\rm th}$-order $m$-point boundary value problems. Mathematica Bohemica, Tome 135 (2010) no. 1, pp. 15-28. doi: 10.21136/MB.2010.140679
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140679/}
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