Geodesic
Existence and iteration of positive solutions for a singular two-point boundary value problem with a $p$-Laplacian operator
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 135-152

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MR Zbl
In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation $(\phi _p(u^{\prime }))^{\prime }+q(t)f(u)=0$, $01$, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient $q(t)$ may be singular at $t=0,1$.
In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation $(\phi _p(u^{\prime }))^{\prime }+q(t)f(u)=0$, $0$, where $\phi _p(s):=|s|^{p-2}s$, $p>1$, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient $q(t)$ may be singular at $t=0,1$.
Classification : 34A45, 34B10, 34B15, 34B18
Keywords: iteration; symmetric and monotone positive solution; nonlinear boundary value problem; $p$-Laplacian 
Ma, De-xiang; Ge, Wei-Gao; Gui, Zhan-Ji. Existence and iteration of positive solutions for a singular two-point boundary value problem with a $p$-Laplacian operator. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 135-152. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a11/
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     year = {2007},
     volume = {57},
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     zbl = {1174.34018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a11/}
}
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[1] J. Wang: The existence of positive solutions for the one-dimensional $p$-Laplacian. Proc. Am. Math. Soc. 125 (1997), 2275–2283. | DOI | MR | Zbl

[2] L.  Kong, J. Wang: Multiple positive solutions for the one-dimensional $p$-Laplacian. Nonlinear Analysis 42 (2000), 1327–1333. | DOI | MR

[3] D. Guo, V. Lakshmikantham: Nonlinear Problems in Abstract. Cones. Academic Press, Boston, 1988. | MR

[4] X.  He, W.  Ge: Twin positive solutions for the one-dimensional $p$-Laplacian. Nonlinear Analysis 56 (2004), 975–984. | DOI | MR | Zbl

[5] R. I. Avery, C. J. Chyan, and J. Henderson: Twin solutions of boundary value problems for ordinary differential equations and finite difference equations. Comput. Math. Appl. 42 (2001), 695–704. | DOI | MR

[6] R. P. Agarwal, H.  Lü and D. O’Regan: Eigenvalues and the one-dimensional $p$-Laplacian. J.  Math. Anal. Appl. 266 (2002), 383–340. | DOI | MR

[7] Y.  Guo, W.  Ge: Three positive solutions for the one-dimensional $p$-Laplacian. Nonlinear Analysis 286 (2003), 491–508. | MR | Zbl

[8] H. Amann: Fixed point equations and nonlinear eigenvalue problems in order Banach spaces. SIAM Rev. 18 (1976), 620–709. | DOI | MR