Existence of positive solutions of singular boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
Positive solutions of singular boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
Existence of multiple positive solutions of singular boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
Quadratic functionals for second order matrix equations on time scales
Non-Linear Analysis
Sturm-Liouville eigenvalue problems on time scales
Applied Mathematics and Computation
On the existence of positive solutions for a class of singular boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
Positive solutions for a nonlinear differential equation on a measure chain
Mathematical and Computer Modelling: An International Journal
On the existence of positive solutions for 2n-order singular boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
On the number of positive solutions of systems of nonlinear dynamic equations on time scales
Journal of Computational and Applied Mathematics
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We consider the even order nonlinear eigenvalue problem (-1)muΔ2m (t) = λf(t,u,(σ(t))), uΔ2i (0) = uΔ2i (σ(1)) = 0, 0 ≤ i ≤ m - 1, on a measure chain T. Results on existence and nonexistence of positive solutions are obtained for λ evaluated in different intervals. Under certain assumptions, the complete scenario for all λ 0 is established. Our work develops and improves many known results in the literature even for the case that T is the real number line. We also interpret our general results on measure chains to the discrete case which yields a new set of conditions for the existence and nonexistence of positive solutions of eigenvalue problems for difference equations.