Monotone Iterative Method and Regular Singular Nonlinear Bvp in the Presence of Reverse Ordered Upper and Lower Solutions
نویسنده
چکیده
Monotone iterative technique is employed for studying the existence of solutions to the second-order nonlinear singular boundary value problem − ` p(x)y′(x) ́′ + p(x)f ` x, y(x), p(x)y′(x) ́ = 0 for 0 < x < 1 and y′(0) = y′(1) = 0. Here p(0) = 0 and xp′(x)/p(x) is analytic at x = 0. The source function f(x, y, py′) is Lipschitz in py′ and one sided Lipschitz in y. The initial approximations are upper solution u0(x) and lower solution v0(x) which can be ordered in one way v0(x) ≤ u0(x) or the other u0(x) ≤ v0(x).
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