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Multiplicity of solutions for a problem involving $1$-biharmonic operator | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 آبان 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.30844.1791 | ||
| نویسندگان | ||
| Mahsa Amoie* 1؛ Mohsen Alimohammady2 | ||
| 1Department of Mathematics, University of Mazandaran | ||
| 2Department of Mathematics, University of Mazandaran Babolsar, Iran | ||
| تاریخ دریافت: 28 آذر 1404، تاریخ بازنگری: 11 مهر 1405، تاریخ پذیرش: 12 مهر 1405 | ||
| چکیده | ||
| The objective of this paper is to establish the existence of two solutions for problems involving the $1$-Laplacian and $1$-biharmonic operators with nonlinearities exhibiting critical growth. More precisely, we prove that the corresponding fourth-order equations involving the $1$-biharmonic operator admit at least two solutions, one of which is radial, while the other is non-radial and non-rotational. | ||
| کلیدواژه‌ها | ||
| $1$- biharmonic operator؛ functions of bounded variation؛ nehari manifold | ||
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