وجود حداقل سه جواب ضعیف برای یک دستگاه شبه‌خطی بیضوی
محورهای موضوعی : آمار
سعید شکوه
1
(استادیار گروه ریاضی، دانشکده علوم پایه، دانشگاه گنبدکاووس، گنبدکاووس، ایران)
کلید واژه: three weak solutions, Boundary value problems, variational method,
چکیده مقاله :
در این مقاله با استفاده از قضیه‌هایی که توسط پروفسور ریچری در مقاله [8] و پروفسور بوناننو در مقاله [6] اثبات شده است، وجود حداقل سه جواب ضعیف را برای یک دستگاه شبه‌خطی بیضوی ثابت خواهیم کرد. در واقع، ما به دستگاه معادله دیفرانسیل یک عملگر غیرخطی مشتق‌پذیر نسبت خواهیم داد به‌طوری‌که نقاط بحرانی این عملگر جواب‌های ضعیف از دستگاه مورد‌نظر باشند.
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system.
[1] G. A. Afrouzi, A. Hadjian, Infinitely many solutions for a class of Dirichlet quasilinear elliptic systems, J. Math. Anal. Appl. 393, 265–272 (2012).
[2] G. A. Afrouzi, A. Hadjian, N. B. Zographopoulos, Multiple nonsemitrivial solutions for a class of degenerate quasilinear elliptic systems, Topological Methods in Nonlinear Analysis, 45, 385–397 (2015) .
[3] G. A. Afrouzi, S. Heidarkhani, Existence of three solutions for a class of Dirichlet quasilinear elliptic systems involving the - Laplacian, Nonlinear Anal. 70, No. 1, 135-143 (2009).
[4] G. A. Afrouzi, S. Heidarkhani, D. O’Regan, Three solutions to class of Neumann doubly eigenvalue elliptic systems driven by a -Laplacian, Bull. Korean Math. Soc. 47, No. 6, 1235-1250 (2010).
[5] G. Anello, G.Cordaro, An existence theorem for the Neumann problem involving the Laplacian, J. Convex Anal. 10, 185-198 (2003).
[6] G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Anal., 54, 651-665 (2003).
[7] A. Kristaly, Existence of two non-trivial solutions a class of quasilinear elliptic variational systems on strip-like domains, Proc. Edinb. Math. Soc. 48, 465-477 (2005).
[8] B. Ricceri, A three critical points theorem revisited,NonlinearAnal., 70, 3084-3089 (2009).
[9] M. Manuela Rodrigues, Multiplicity of solutions on a nonlinear eigenvalue problem for - Laplacian- like operators, Mediterr. J. Math., 9, 211-223 (2012).
