Integro-differential systems with variable exponents of nonlinearity

Abstract

Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.

Keywords

• nonlinear parabolic equation
• integro-differential equation
• generalized lebesgue space
• generalized sobolev space
• variable exponents of nonlinearity
• 47g20
• 46e35
• 35k52
• 35k55