Positive Solutions of Boundary Value Problems for Second Order Singular Nonlinear Differential Equations
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摘要: 分别在0≤f0+<M1,m1<f∞-≤∞和0≤f∞+<M1,m1<f0-≤∞的情形下研究了非线性奇异边值问题u″+g(t)f(u)=0,0<t<1,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0正解的存在性,其中f0+=0f(u)/u,f∞-=∞f(u)/u,f0-=0f(u)/u,f∞+=∞f(u)/u,g在区间[0,1]的端点可以具有奇性。Abstract: New existence results are presented for the singular second order nonlinear boundary value problems u″+g(t)f(u)=0,0<t<1,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0 under the conditions 0≤f0+<M1,m1<f∞-≤∞ or 0≤f∞+<M1,m1<f0-≤∞,where f0+=0f(u)/u,f∞-=∞f(u)/u,f0-=0f(u)/u,f∞+=∞f(u)/u,g may be singular at t=0 and/or t=1.The proof uses a fixed point theorem in cone theory.
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Key words:
- second order singular boundary value problems /
- positive solutions /
- cone /
- fixed point
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[1] Erbe L H, WANG Hai-yan. On the existence of positive solutions of ordinary differential equations[J]. Proc Amer Math Soc,1994,120(3):743-748. [2] 马如云. 奇异二阶边值问题的正解[J]. 数学学报,1998,41(6):1225-1230. [3] Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces[J]. SIAM Rev,1976,18(4):620-709. [4] 郭大钧. 非线性泛函分析[M]. 济南:山东科技出版社,1985.
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