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On a class of infinite semipositone problems via Sub and Supersolutions method | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 آذر 1404 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2025.30380.1778 | ||
| نویسنده | ||
| Saleh Shakeri* | ||
| Ayatollah Amoli Branch, Islamic Azad University | ||
| تاریخ دریافت: 05 آبان 1404، تاریخ بازنگری: 17 آذر 1404، تاریخ پذیرش: 17 آذر 1404 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Kirchhoff-type problems؛ Infinite semipositone؛ Sub and Supersolutions method | ||
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