Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem

Avery, Richard I.; Davis, John M.; Henderson, Johnny

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Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem

Avery, Richard I. ; Davis, John M. ; Henderson, Johnny

Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Résumé

Summary: We study the existence of solutions to the fourth order Lidstone boundary value problem $$\displaylines{ y^{(4)}(t) = f(y(t),-y''(t)),\cr y(0)=y''(0)=y''(1)=y(1)=0\,. }$$ By imposing growth conditions on $f$ 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.

Classification : 34B18, 34B27, 39A12, 39A99
Keywords: lidstone boundary value problem, Green's function, multiple solutions, fixed points, difference equation

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     author = {Avery, Richard I. and Davis, John M. and Henderson, Johnny},
     title = {Three symmetric positive solutions for {Lidstone} problems by a generalization of the {Leggett-Williams} theorem},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a56/}
}

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Avery, Richard I.; Davis, John M.; Henderson, Johnny. Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a56/