The literature concerning nonlocal boundary value problems is extensive. Moreover, applications of fixed point theorems to positive solutions of such has sparked much interest, see [9, 10, 11, 12]. Many of the results involving nonlocal boundary value problems are summarized in [9]. A more general summary of positive solutions results for a variety of differential equation types is available in...

The purpose of this paper is to compare the solutions of one-dimensional boundary value problems corresponding to classical, fractional and nonlocal diffusion on bounded domains. The latter two diffusions are viable alternatives for anomalous diffusion, when Fick’s first law is an inaccurate model. In the case of nonlocal diffusion, a generalization of Fick’s first law in terms of a nonlocal fl...

Let be a an open bounded domain in R , N 2; with a smooth boundary @ ; and T > 0. De…ne D = (0; T ) and = @ [0; T ]: In this paper we are concerned with the existence of solutions of the following parabolic inclusion ut + Lu 2 F (x; t; u), (x; t) 2 D; u(x; t) = 0; (x; t) 2 subjected to the nonlocal condition u(x; 0) = R T 0 g(x; t; u(x; t))dt for x 2 : We provide su¢ cient conditions on L; F; g...