Existence of multiple symmetric positive solutions of higher order Lidstone problems
نویسندگان
چکیده
منابع مشابه
Positive Solutions for Higher Order Lidstone Boundary Value Problems. a New Approach via Sperner’s Lemma
Consider the higher order nonlinear scalar differential equations (0.1) x(t) = −f(t, x(t), ..., y(t), ...y(2(n−1))(t)), 0 ≤ t ≤ 1 where f ∈ C([0, 1] × R+, R+), R+ = [0,∞) associated to the Lidstone boundary conditions (0.2) x(0) = 0 = x(1), (0.3) x(0) = 0 = x(1). Existence of a solution of boundary value Problems (BVP) (0.1)-(0.2) such that x(t) > 0, 0 < t < 1, i = 0, 1, ..., n− 1 are given, un...
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where n≥ is an integer, f : (, )× (,∞)→ [,∞) is continuous, αi, βi are nonnegative constants, α i + αiβi > , i = , . . . ,n. f (t,u) may be singular at u = , t = (and/or t = ). If a function u : [, ]→ R is continuous and satisfies u(t) = u( – t) for t ∈ [, ], then we say that u(t) is symmetric on [, ]. By a symmetric positive solution of BVP (.) we mean a symmetric functi...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2003
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(03)00386-x