The existence and compactness of the set of solutions for a 2-order nonlinear integrodifferential equation in N variables in a Banach space



	The existence and compactness of the set of solutions for a 2-order nonlinear integrodifferential equation in N variables in a Banach space


	Fixed Point Theory, Volume 23, No. 2, 2022, 607-632, June 15th, 2022 DOI: 10.24193/fpt-ro.2022.2.12 Authors: Le Thi Phuong Ngoc and Nguyen Thanh Long Abstract: In this paper, by applying the fixed point theorem of Krasnosel'skii, we prove the existence and compactness of the set of solutions for a 2-order nonlinear integrodifferential equation in N variables in an arbitrary Banach space E. Here, an appropriate Banach space X₁ for the above equation is defined and a sufficient condition for relatively compact subsets in X₁ is proved. An example is given to verify the efficiency of the used method. Key Words and Phrases: Nonlinear integrodifferential equation in N variables, the fixed point theorem of Krasnosel'skii. 2010 Mathematics Subject Classification: 45G10, 47H10, 47N20, 65J15. Published on-line: June 15th, 2022. Abstract pdf Fulltext pdf Back to volume's table of contents