Generalized multipoint conjugate eigenvalue problems

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Positive solutions and nonlinear multipoint conjugate eigenvalue problems ∗

Values of λ are determined for which there exist solutions in a cone of the n order nonlinear differential equation, u = λa(t)f(u), 0 < t < 1, satisfying the multipoint boundary conditions, u(ai) = 0, 0 ≤ j ≤ ni−1, 1 ≤ i ≤ k, where 0 = a1 < a2 < · · · < ak = 1, and ∑k i=1 ni = n, where a and f are nonnegative valued, and where both lim |x|→0+ f(x)/|x| and lim |x|→∞ f(x)/|x| exist.

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For the nth order nonlinear differential equation y(n)(t) = f(y(t)), t ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, y(ai) = 0, 1 ≤ i ≤ k, 0 ≤ j ≤ ni − 1, 0 = a1 < a2 < · · · < ak = 1, and ∑k i=1 ni = n, where f : R→ [0,∞) is continuous, growth condtions are imposed on f which yield the existence of at least three solutions that belong to a cone.

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ژورنال

عنوان ژورنال: Mathematical and Computer Modelling

سال: 2000

ISSN: 0895-7177

DOI: 10.1016/s0895-7177(00)00168-0