Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives
Abstract
We study the existence of monotone positive solutions for the semipositone right focal boundary value problems ⎧⎪⎪⎨ ⎪⎪⎩ (−1)(n−k)u(n)(t) = λf(t, u(t), u (t), . . . , u(k−1)(t)), t∈ (0, 1), u(i)(0) = 0, 0 ≤ i ≤ k − 1, u(j)(1) = 0, k≤ j ≤ n − 1, where λ > 0 is a parameter, n ≥ 3, 1 < k ≤ n − 1 is fixed, f may change sign for 0 < t < 1 and we allow f is both semipositone and lower unbounded. Without making any monotone type assumption, the existence results of at least one and two monotone positive solutions are obtained by means of the fixed point theorems in cones.
Citation
Hao, X. and Liu, L. and Wu, Y.H. 2012. Existence of Monotone Positive Solutions for semipositone right focal boundary value problems with dependence on the derivatives. Acta Mathematica Sinica, Chinese Series. 55 (1): pp. 150160.
Source Title
Acta Mathematica Sinica, Chinese Series
ISSN
School
Department of Mathematics and Statistics
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