On a structure of the set of positive solutions to second-order equations with a super-linear non-linearity
Keyword(s):
Abstract We study the existence and multiplicity of positive solutions to the periodic problem u ′′ = p ( t ) u - q ( t , u ) u + f ( t ) ; u ( 0 ) = u ( ω ) , u ′ ( 0 ) = u ′ ( ω ) , u^{\prime\prime}=p(t)u-q(t,u)u+f(t);\quad u(0)=u(\omega),\quad u^{\prime}(0)=u^{\prime}(\omega), where p , f ∈ L ( [ 0 , ω ] ) p,f\in L([0,\omega]) and q : [ 0 , ω ] × R → R q\colon[0,\omega]\times\mathbb{R}\to\mathbb{R} is a Carathéodory function. By using the method of lower and upper functions, we show some properties of the solution set of the considered problem and, in particular, the existence of a minimal positive solution.
2013 ◽
2012 ◽
Vol 2012
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pp. 1-13
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2003 ◽
Vol 281
(1)
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pp. 99-107
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2012 ◽
Vol 63
(9)
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pp. 1369-1381
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2001 ◽
Vol 22
(12)
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pp. 1476-1480
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