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An existence result of three solutions for a $\mathbf{2n}$-th-order boundary-value problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 52، دوره 12، شماره 1، مرداد 2021، صفحه 679-691 اصل مقاله (435.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4870 | ||
| نویسندگان | ||
| Osman Halakoo1؛ Mahdi Azhini* 2؛ Ghasem Afrouzi3 | ||
| 1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| 3Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| تاریخ دریافت: 15 آبان 1397، تاریخ بازنگری: 21 اسفند 1397، تاریخ پذیرش: 23 مرداد 1398 | ||
| چکیده | ||
| In this paper, we establish the existence of at least three weak solutions for some one-dimensional $2n$-th-order equations in a bounded domain. A particular case and a concrete example are then presented. | ||
| کلیدواژه‌ها | ||
| Boundary value problem؛ Sobolev space؛ Critical point؛ Three solutions؛ Variational method | ||
| مراجع | ||
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[1] G.A. Afrouzi and S. Heidarkhani, Three solutions for a quasilinear boundary value problem, Nonlinear Anal. TMA. 69 (2008) 3330–3336. [2] G.A. Afrouzi, S. Heidarkhani and D.O’Regan, Existence of three solutions for a doubly eigenvalue fourth-order boundary value problem, Taiwanese J. Math. 15 (2011) 201–210. [3] D. Averna and G. Bonanno, Three solutions for quasilinear two-point boundary value problem involving the onedimensional p-Laplacian Proc. Edinb. Math. Soc. 47 (2004) 257–270. [4] G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Anal. 54 (2003) 651–665. [5] G. Bonanno and B. Di Bella, A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl. 343 (2008) 1166–1176. [6] O. Halakoo, G.A. Afrouzi and M. Azhini, An existence result of three solutions for a fourth-order boundary-value problem, Submitted. [7] R. Livrea, Existence of three solutions for a quasilinear two-point boundary value problem, Arch. Math. 79 (2002) 288–298. [8] L.A. Peletier, W.C. Troy and R.C.A.M. Van der Vorst, Stationary solutions of a fourth-order nonlinear diffusion equation, (Russian) Translated from the English by V. V. Kurt. Differentsialnye Uravneniya 31 (1995) 327–337. English translation in Differential Equations 31 (1995) 301–314. [9] B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 70 (2009) 3084–3089. [10] G. Talenti, Some inequalities of Sobolev type on two-dimensional spheres, W. Walter (ed.), General Inequalities, Vol. 5, Int. Ser. Numer. Math., Birkhauser, Basel, 80 (1987) 401–408. [11] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II/B and III, Berlin-Heidelberg-New York, 1990 and 1985. | ||
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