Showing papers by "Binlin Zhang published in 2014"

Existence of weak solutions for non-local fractional problems via Morse theory

Abstract: In this paper, we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. Non-trivial solutions are obtained by computing the critical groups and Morse theory. Our results extend some classical theorems for semilinear elliptic equations to the non-local fractional setting.

Morse theory and local linking for a nonlinear degenerate problem arising in the theory of electrorheological fluids

Abstract: Many electrorheological fluids are suspensions of solid particles that are exposed to a strong electric field. This causes a dramatic increase of their effective viscosity. In this paper we are concerned with a mathematical problem that is related with this non-Newtonian behavior. More precisely, we study the nonlinear stationary equation − div ( | ∇ u | p ( x ) − 2 ∇ u ) + | u | p ( x ) − 2 u = f ( x , u ) in Ω , under Dirichlet boundary conditions, where Ω is a smooth bounded domain in R n , p > 1 is a continuous function, and f ( x , u ) has a sublinear growth near the origin. Under various natural assumptions, by using the Morse theory in combination with local linking arguments, we obtain the existence of nontrivial weak solutions.

The Stationary Navier-Stokes Equations in Variable Exponent Spaces of Clifford-Valued Functions

Abstract: In the frame of variable exponent spaces of Clifford-valued functions and using the Banach fixed-point theorem, we obtain the existence and uniqueness of solutions to the stationary Navier-Stokes equations and Navier-Stokes equations with heat conduction under certain assumptions. In a sense, we extend some results of P. Cerejeiras and U. Kahler [P. Cerejeiras and U. Kahler, Elliptic boundary value problems of fluid dynamics over unbounded domains, Mathematical Methods in the Applied Sciences, 23(2000), 81-101].