Geodesic
Global structure of positive solutions for superlinear $2m$th-boundary value problems
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 161-172 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider boundary value problems for nonlinear $2m$th-order eigenvalue problem $$ \begin{aligned} (-1)^mu^{(2m)}(t)=\lambda a(t)f(u(t)),\ \ \ \ \ 00$ for some $t_0\in [0,1]$, $f\in C([0,\infty ),[0,\infty ))$ and $f(s)>0$ for $s>0$, and $f_0=\infty $, where $f_0=\lim _{s\rightarrow 0^+}f(s)/s$. We investigate the global structure of positive solutions by using Rabinowitz's global bifurcation theorem.
We consider boundary value problems for nonlinear $2m$th-order eigenvalue problem $$ \begin{aligned} (-1)^mu^{(2m)}(t)=\lambda a(t)f(u(t)),\ \ \ \ \ 01, \\ u^{(2i)}(0)=u^{(2i)}(1)=0,\ \ \ \ i=0,1,2,\cdots ,m-1 . \end{aligned} $$ where $a\in C([0,1], [0,\infty ))$ and $a(t_0)>0$ for some $t_0\in [0,1]$, $f\in C([0,\infty ),[0,\infty ))$ and $f(s)>0$ for $s>0$, and $f_0=\infty $, where $f_0=\lim _{s\rightarrow 0^+}f(s)/s$. We investigate the global structure of positive solutions by using Rabinowitz's global bifurcation theorem.
Classification : 34B08, 34B10, 34B18, 34G20, 47J15, 47N20
Keywords: multiplicity results; Lidstone boundary value problem; eigenvalues; bifurcation methods; positive solutions 
@article{CMJ_2010_60_1_a13,
     author = {Ma, Ruyun and An, Yulian},
     title = {Global structure of positive solutions for superlinear $2m$th-boundary value problems},
     journal = {Czechoslovak Mathematical Journal},
     pages = {161--172},
     year = {2010},
     volume = {60},
     number = {1},
     mrnumber = {2595080},
     zbl = {1224.34034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_1_a13/}
}
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Ma, Ruyun; An, Yulian. Global structure of positive solutions for superlinear $2m$th-boundary value problems. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 161-172. http://geodesic.mathdoc.fr/item/CMJ_2010_60_1_a13/