Controllability for a class of second-order evolution differential inclusions without compactness

ABSTRACT

In this paper, we discuss the existence and controllability for a class of second-order evolution differential inclusions without compactness in Banach spaces. By applying the technique of weak topology and Glicksberg–Ky Fan fixed point theorem, we prove our main results without the hypotheses of compactness on the operator generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Further, we extend our study to existence and controllability of second-order evolution differential inclusions with nonlocal conditions and impulses. Finally, an example is given for the illustration of the obtained theoretical results.

KEYWORDS:

• Existence
• controllability
• cosine function of operators
• second-order evolution inclusions
• multivalued map

AMS SUBJECT CLASSIFICATIONS:

• 34K05
• 34K30
• 35R10
• 47H04
• 93B05

Notes

No potential conflict of interest was reported by the authors.