In the theory of differential equations, the basic concepts have been formulated studying the problems of classical mathematical physics. However, the modern problems motivate to formulate and investigate the new ones, for example, a class of nonlocal problems. Nonlocal conditions arise when we cannot measure data directly at the boundary. In this case, the problem is formulated, where the valu...

The positivity of solutions for parabolic problems is the base of comparison principle which is important in monotonic methods used for these problems. Recently, Yin [1] developed several results in applications of the comparison principle, especially on nonlocal problems. Earlier works on problems with nonlocal boundary conditions can be found in [2], and some of references can be found in [1,...

This paper is concerned with the existence of mild solutions to a class of semilinear differential inclusions with nonlocal conditions. By using the fixed point theory for multivalued maps, we get some general results on nonlocal differential inclusions, which include some recent results on nonlocal problems as special cases. An example of partial differential equations is provided to illustrat...

This is a study of a class of nonlocal nonlinear diffusion equations (NNDEs). We present several new qualitative results for nonlocal Dirichlet problems. It is shown that solutions with positive initial data remain positive through time, even for nonlinear problems; in addition, we prove that solutions to these equations obey a strong maximum principle. A striking result shows that nonlocal sol...

The positivity of solutions for parabolic problems is the base of comparison principle which is important in monotonic methods used for these problems. Recently, Yin [1] developed several results in applications of the comparison principle, especially on nonlocal problems. Earlier works on problems with nonlocal boundary conditions can be found in [2], and some of references can be found in [1,...

The present paper deals with the eigenvalue problems for oneand two-dimensional second order differential operators with given nonlocal coupled boundary conditions. The corresponding finite-difference (discrete) problems have been investigated in the paper [1]. First of all, we will consider the eigenvalue problem for one-dimensional differential operator with given nonlocal coupled boundary co...