Positive solutions and conjugate points for multipoint boundary value problems
نویسندگان
چکیده
منابع مشابه
Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems
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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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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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1992
ISSN: 0022-0396
DOI: 10.1016/0022-0396(92)90041-k