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Zbl 1110.34016
Ma, Dexiang; Han, Jianxin; Chen, Xuegang
Positive solution of three-point boundary value problem for the one-dimensional $p$-Laplacian with singularities. (English)
[J] J. Math. Anal. Appl. 324, No. 1, 118-133 (2006). ISSN 0022-247X

Summary: We deal with positive solutions of the following nonlinear three-point singular boundary value problem with a $p$-Laplacian operator $$\bigl( \varphi_p(u') \bigr)'+q(t)f(t,u)=0,\quad 0<t<1,$$ subject to $$u(0)-g \bigl(u'(0)\bigr)=0,\quad u(1)-\beta u(\eta)=0,$$ or $$u(0)-\alpha u (\eta)=0,\quad u(1)-g\bigl(u'(1)\bigr) =0,$$ where $f(t,u)$ may be singular at $u=0$ and $q(t)$ may be singular at $t=0,1$. New existence principles are established.

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
34B16 Singular nonlinear boundary value problems
34B10 Multipoint boundary value problems

Keywords: singularity; positive solution; nonlinear boundary conditions; $p$-Laplacian

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