Existence of multiple positive solutions of singular boundary value problems

Existence and multiplicity of solutions for some three-point nonlinear boundary value problems

“…For example, Ma and Castaneda [7] using the well-known fixed point theorem in cones established some results on the existence of at least one positive solution for some m-point boundary value problems if the nonlinearity f is either superlinear or sublinear. The purpose of this paper is to X. Xian and D. O'Regan 3 extend the main results of [1,2,5,9] to the nonlinear three-point BVP (1.1 λ ). We will consider the existence and multiplicity of positive solution for the nonlinear three-point BVP (1.1 λ ).…”

“…Theorem 1.4 (see [5] Xu and Ma [12] generalized the main results of [1,2,5,9] to an operator equation in a real Banach space E. In recent years, the multipoint BVP has been extensively studied (see [3, 4, 6-8, 10, 11, 13] and the references therein). For example, Ma and Castaneda [7] using the well-known fixed point theorem in cones established some results on the existence of at least one positive solution for some m-point boundary value problems if the nonlinearity f is either superlinear or sublinear.…”

“…The BVP (1.2 λ ) has been studied extensively in the literature, see [1,2,5,9,12] and the references therein. Choi [1] studied the particular case where f (u) = e u , a ∈ C 1 (0,1], a > 0 in (0,1), and a can be singular at t = 0, but is at most O(1/t 2−δ ) as t → 0 + for some δ.…”

The existence of multiple positive solutions for a class of semipositone Dirichlet boundary value problems

“…Nonlinear boundary value problems, as an important branch of modern applied mathematics, have been studied by many authors in recent years [1,4,[7][8][9][10][11]. In the study The second author is financially supported by the National Natural Science Foundation of China (11071141, 10771117) and the Natural Science Foundation of Shandong Province of China (Y2007A23, ZR2010AM017).…”

Existence of positive solutions for singular four-point boundary value problem with a p-Laplacian

“…They also appear in the study of positive radial solutions of nonlinear elliptic equations. Therefore, they have been extensively studied in recent years, see, for instance, [1]- [5], [8], [13] and references therein. After studying singular two-point BVPs in detail, some authors began to pay attention to singular multi-point BVPs [9]- [12], [14]- [17].…”