Geodesic
Positive solutions for third-order Sturm-Liouville boundary-value problems with \(p\)-Laplacian
Electronic journal of differential equations, Tome 2009 (2009)
In this article, we consider the third-order Sturm-Liouville boundary value problem, with

$\displaylines{ (\phi_p(u''(t)))'+f(t,u(t))=0, \quad t\in (0,1),\cr \alpha u(0)-\beta u'(0)=0,\quad \gamma u(1)+\delta u'(1)=0,\quad u''(0)=0, }$

where $\phi_p(s)=|s|^{p-2}s, p>1$. By means of the Leggett-Williams fixed-point theorems, we prove the existence of multiple positive solutions. As an application, we give an example that illustrates our result.
Classification : 34K10
Keywords: positive solution, Sturm-Liouville boundary value problem, p-Laplacian operator, concave functional, fixed point 
@article{EJDE_2009__2009__a71,
     author = {Zhai,  Chengbo and Guo,  Chunmei},
     title = {Positive solutions for third-order {Sturm-Liouville} boundary-value problems with {\(p\)-Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1186.34035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a71/}
}
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Zhai,  Chengbo; Guo,  Chunmei. Positive solutions for third-order Sturm-Liouville boundary-value problems with \(p\)-Laplacian. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a71/