Three Symmetric Positive Solutions for Lidstone Problems by a Generalization of the Leggett-Williams Theorem
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We study the existence of solutions to the fourth order Lidstone boundary value problem y(4)(t) = ƒ(y(t), -y" (t)), y(0) = y"(0) = y"(1) = y(1) = 0. By imposing growth conditions on ƒ and using a generalization of the multiple fixed point theorem by Leggett and Williams, we show the existence of at least three symmetric positive solutions. We also prove analogous results for difference equations.
CitationAvery, R. I., Davis, J. M., & Henderson, J. (2000). Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem. Electronic Journal of Differential Equations, 2000(40), pp. 1-15.
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