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Positive Solutions of Boundary Value Problems for Second-Order Singular Nonlinear Differential Equations

Authors:	Ren-gui Li Li-shan Liu

Affiliation:	Department of Mathematics, Qufu Normal University, Qufu 273165, P R China

Abstract:	New existence results are presented for the singular second-order nonlinear boundary value problems u″+g(t)f(u)=0, 00 ⁺ 1, m₁∞ ⁻ ≤∞ or 0≤f _∞ ⁺ 1, m₁0 ⁻ ≤∞, where $begin{gathered} f_0^ + = overline {lim } _{u to 0} f(u)/u, f_infty ^ - = underline {lim } _{u to infty } f(u)/u, f_0^ - = hfill underline {lim } _{u to 0} f(u)/u, f_infty ^ + = overline {lim } _{u to infty } f(u)/u hfill end{gathered}$ , g may be singular at t=0 and/or t=1. The proof uses a fixed point theorem in cone theory. Foundation item: the National Natural Science Foundation of China (19871048); the Natural Science Foundation of Shandong Province (Y98A09012) Biography: Li Ren-gui (1968-), Lecturer, Master

Keywords:	second_order singular boundary value problems positive solutions cone fixed point
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