A class of second-order nonlocal indefinite impulsive differential systems

Abstract

1 0 g(t)y(t) dt, y (1) = 0, where the weight functions a(t), b(t), and ω(t) change sign on [0, 1], and g(t) ≡ 0 and h(t) ≡ 0 on [0, 1]. By constructing a cone K 1 × K 2 , which is the Cartesian product of two cones in space PC[0, 1], and applying the well-known fixed point theorem of cone expansion and compression in K 1 × K 2 , we obtain conditions for the existence and multiplicity of positive solutions of a nonlocal indefinite impulsive differential system. An example is given to illustrate the main results.

Multiple positive solutions to singular fractional differential equations with integral boundary conditions involving $p-q$-order derivatives

“…The existence of positive solutions for FDEs integral boundary problems (BVPs) with one or two parameters in boundary conditions is obtained by means of fixed point theory [5,14,22,28]. The existence of positive solutions for integer-order differential equations with integral boundary conditions can be found in the literature (see [8,13,15,18,24] for instance). As is well known, semipositone problems arise in bulking of mechanical systems, chemical reactions, astrophysics, combustion, management of natural resources, etc.…”

Positive radial solutions of n-dimensional elliptic systems with indefinite weight functions and n parameters

“…The study of boundary value problems with positive solutions has attracted recently the attention of different researchers and it is a topic of current interest; see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], and the references therein.…”