On a class of infinite semipositone problems via Sub and Supersolutions method

Document Type : Research Articles

Author

Ayatollah Amoli Branch, Islamic Azad University

10.22080/cjms.2025.30380.1778

Abstract

Using the method of sub-super solutions, we study the existence of positive solutions for a class of infinite semipositone problems involving nonlocal operator.The concepts of sub- and super-solution were introduced
by Nagumo in 1937 who proved, using also the shooting method, the existence
of at least one solution for a class of nonlinear Sturm-Liouville problems. In fact, the premises of the sub- and
super-solution method can be traced back to Picard. He applied, in the early 1880s, the method of successive
approximations to
argue the existence of solutions for nonlinear elliptic equations that are suitable
perturbations of uniquely solvable linear problems. This is the starting point of
the use of sub- and super-solutions in connection with monotone methods. Picard's techniques were applied later by
Poincar'e in connection with problems arising in astrophysics.

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