This special issue is the very first journal issue specially dedicated to the theory of variable Lebesgue and Sobolev spaces and applications of this theory to the study of nonlinear differential equations with nonstandard growth. In the recent decades, this theory has been developing very rapidly and has already achieved a certain grade of maturity. Apart from purely mathematical interest, importance, and attractiveness, the theory finds numerous applications in the mathematical modeling of the real-world processes such as filtration, flows of electrorheological and non-Newtonian fluids, or algorithms for the processing of digital images.

We invite the researchers working in this area and the affine fields to contribute original research articles as well as the review articles which would stimulate the continuing work in challenging issues of this branch of mathematics and highlight the state-of-the-art results. Potential topics include, but are not limited to:

• Recent developments in the PDEs with nonstandard growth
• Advances in ODE with variable nonlinearity
• Real-world applications of the differential equations with nonstandard growth
• Calculus of variations in variable Lebesgue and Sobolev spaces
• Numerical analysis

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/ijde/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/ according to the following timetable: