General Lidstone problems: Multiplicity and symmetry of solutions

[摘要] For the 2mth order Lidstone boundary value problem, y((2m))(t) = f(y(t), y(t),..., y((2f))(t),...,y((2(m-1)))(t)), t is an element of [0,1], y((2f))(0) = y((2i))(1) = 0, 0 less than or equal to i less than or equal to m-1, where (-1)(m)f: R-m --> [0, infinity) is continuous, growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions. This generalizes earlier papers which have applied Avery's generalization of the Leggett-Williams theorem to Lidstone problems. We then prove the analogous result for difference equations. (C) 2000 Academic Press.

[发布日期] 2000-11-15

[关键词] Lidstone boundary value problem;Green's function;multiple solutions;fixed points;difference equation