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Remarks on existence of positive solutions of some integral equations

Jan Ligęza (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We study the existence of positive solutions of the integral equation x ( t ) = μ 0 1 k ( t , s ) f ( s , x ( s ) , x ' ( s ) , ... , x ( n - 1 ) ( s ) ) d s , n 2 in both C n - 1 [ 0 , 1 ] and W n - 1 , p [ 0 , 1 ] spaces, where p 1 and μ > 0 . Throughout this paper k is nonnegative but the nonlinearity f may take negative values. The Krasnosielski fixed point theorem on cone is used.

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