EXISTENCE OF POSITIVE SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS WITH SINGULARITIES IN PHASE VARIABLES
2004 ◽
Vol 47
(1)
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pp. 1-13
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Keyword(s):
AbstractThe singular boundary-value problem $(g(x'))'=\mu f(t,x,x')$, $x'(0)=0$, $x(T)=b>0$ is considered. Here $\mu$ is the parameter and $f(t,x,y)$, which satisfies local Carathéodory conditions on $[0,T]\times(\mathbb{R}\setminus\{b\})\times(\mathbb{R}\setminus\{0\})$, may be singular at the values $x=b$ and $y=0$ of the phase variables $x$ and $y$, respectively. Conditions guaranteeing the existence of a positive solution to the above problem for suitable positive values of $\mu$ are given. The proofs are based on regularization and sequential techniques and use the topological transversality theorem.AMS 2000 Mathematics subject classification: Primary 34B16; 34B18
2005 ◽
Vol 48
(1)
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pp. 1-19
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2005 ◽
Vol 29
(2)
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pp. 235-247
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2001 ◽
Vol 162
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pp. 127-148
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2007 ◽
Vol 50
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pp. 217-228
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2007 ◽
Vol 325
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pp. 517-528
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1998 ◽
Vol 39
(3)
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pp. 386-407
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2013 ◽
Vol 16
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