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- W2027203199 abstract "In this work it is presented an existence result for the impulsive problem composed by the fourth order fully nonlinear equation $$begin{aligned} u^{left( ivright) }left( xright) =fleft( x,uleft( xright) ,u^{prime }left( xright) ,u^{prime prime }left( xright) ,u^{prime prime prime }left( xright) right) end{aligned}$$ for a.e. $$xin left[ 0,1right] ~backslash ~left{ x_{1},ldots ,x_{m}right} $$ where $$f:left[ 0,1right] times mathbb {R} ^{4}rightarrow mathbb {R}$$ is a $$L^{1}$$ -Carathéodory function, along with the periodic boundary conditions $$begin{aligned} u^{left( iright) }left( 0right) =u^{left( iright) }left( 1right) , quad i=0,1,2,3, end{aligned}$$ and the impulses $$begin{aligned} begin{array}{c} uleft( x_{j}^{+}right) =g_{j}left( uleft( x_{j}right) right) , u^{prime }left( x_{j}^{+}right) =h_{j}left( u^{prime }left( x_{j}right) right) , u^{prime prime }left( x_{j}^{+}right) =k_{j}left( u^{prime prime }left( x_{j}right) right) , u^{prime prime prime }left( x_{j}^{+}right) =l_{j}left( u^{prime prime prime }left( x_{j}right) right) , end{array} end{aligned}$$ where $$x_{j}in left( 0,1right) ,$$ for $$j=1,ldots ,m,$$ such that $$ 0=x_{0}<x_{1}<cdots <x_{m}<x_{m+1}=1$$ , and $$g_{j},~h_{j},~k_{j}$$ , $$l_{j}$$ are given real valued functions satisfying some adequate conditions. The arguments used apply lower and upper solutions technique combined with an iterative and non monotone technique." @default.
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- W2027203199 date "2013-11-07" @default.
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- W2027203199 title "Fourth Order Impulsive Periodic Boundary Value Problems" @default.
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- W2027203199 doi "https://doi.org/10.1007/s12591-013-0186-2" @default.
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