It is well known that the classical Schauder fixed point principle plays an important role in proving the existence of solutions both of differential and integral equations. Obviously the basic tool exploited in that fixed point principle is the compactness of operators associated with investigated equations. Apart from the aforementioned Schauder fixed point principle, there exist several other theorems and methods used in the theory of differential and integral equations which are based on compactness conditions. For example, Krasnosel'skii fixed point theorem and its numerous generalizations as well as Arino-Gautier-Penot fixed point theorem for weakly sequentially continuous operators utilize the methods and reasonings associated with compactness conditions. It is worthwhile mentioning that the technique of measures of noncompactness, which is widely used in the last decades, is realized essentially via compactness conditions. Recently, there appeared several research papers treating various aspects of operator theory with help of the use of compactness or weak compactness conditions in connection with applications to the theory of differential and integral equations.

We invite authors to supply original research as well as review articles concerning numerous topics in which compactness conditions play an important role. We are especially interested in paper showing the applicability of compactness conditions in the theory of differential and integral equations. The papers indicating new directions of the investigations with the use of compactness conditions are also warmly invited. Potential topics include, but are not limited to:

• Fixed point theorems based on compactness and weak compactness argumentations
• Applications of compactness conditions in proving existence theorems for differential equations
• Nonlinear integral equations of various type via the compactness conditions
• Finite and infinite systems of differential and integral equations with the use of compactness conditions
• The technique of measures of noncompactness and its application to the theory of differential and integral equations

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