Some Singular Nonlinear Boundary Value Problems

Existence results for superlinear semipositone BVP’s

“…Here we do not assume that f (t, u) is decreasing in u, thus extending the corresponding results in [2,4,6,9]. Our proofs are quite simple and are based on fixed point theorems in a cone.…”

“…The result in [6], which extends the one in [9], requires that f satisfy (A.2), (A.5), (A.8), (A.9), f (t, u) → 0 as u → ∞ and f (t, u) → ∞ as u → 0 uniformly on compact subsets of (r, R), and f (t, u) be decreasing in u for each t. In [4], (A.8) and the limiting conditions of [6] were removed, provided a, b, c, and d are positive. Also, the result in [2] when applied to the problem (1.1) with p(t) = 1 requires that f (t, u) be decreasing in u and f satisfy (A.7). Thus Theorem 3.1 unifies and extends the corresponding results in [2,4,6,9].…”

“…Also, the result in [2] when applied to the problem (1.1) with p(t) = 1 requires that f (t, u) be decreasing in u and f satisfy (A.7). Thus Theorem 3.1 unifies and extends the corresponding results in [2,4,6,9].…”

Existence of multiple positive solutions of singular nonlinear boundary value problems

“…The theorem has been extended to much more general nonlinearities f (t, y) in [11][12][13]. We emphasize that these papers all required that f (t, y) be decreasing in y for fixed t.…”

Nonlinear Superlinear Singular and Nonsingular Second Order Boundary Value Problems

“…We remark at this point that almost all the literature [1,5,10 16] on singular problems is devoted to the case f (t, u, z)# f (t, u). Only very specific situations [2,3,9,10,13] have been examined in the more general situation (i.e. in the case f (t, y, py$)).…”