Existence of principal eigensurfaces for cooperative \((p_1, . . . , p_n)\)-biharmonic systems

Lawouè Robert Toyou; Jonas Doumate; Liamidi Leadi

doi:10.26637/mjm1301/004

Abstract

In this work, we establish existence of principal eigensurface as well as simplicity result for a biharmonician system subject to Navier boundary condition using eigencurve approach.

Keywords:

Nonlinear eigenvalue problems, Variational methods, (p1, · · · , pn)-biharmonic systems, Navier condition.

Mathematics Subject Classification:

35A15, 35J35, 35J58, 35P30

Authors Imprint References Funding Related Articles Downloads

Lawouè Robert Toyou Haute ´Ecole de Commerce et de Management, B´enin
Jonas Doumate Faculté des Sciences et Techniques, Département de Mathématiques, Université d'Abomey-Calavi https://orcid.org/0000-0002-8043-2801
Liamidi Leadi Institut de Math´ematiques et de Sciences Physiques, Universit´e d’Abomey-Calavi, B´enin.

Pages: 26-36
Date Published: 01-01-2025
Vol. 13 No. 01 (2025): Malaya Journal of Matematik (MJM)

R. A. ADAMS: Sobolev Spaces. Academic Press, New York, 1975.

J. BENEDIKT: Uniqueness theorem for p-biharmonic equations. Electron. J. Differential equations 53 (2002), 1-17.

J. BENEDIKT: On the discretness of the spectra of the Dirichlet and Neumann p-biharmonic problem. Abstr. Appl. Anal. 293 (2004), 777-792.

T.J. Doumate, L. R. Toyou, L. A. Leadi: Existence results for (p1, · · · , pn)−biharmonic Systems underNavier boundary condition. Malaya J. Mat. 10 (01) (2022), 63-78.

T. J. DOUMATE, L. R. TOYOU, L. A. LEADI: On Eigensurface of p−biharmonic operator and associated concave-convex type equation. Gulf Journal of Mathematics Vol13, Issue1(2022) 54-87.

T. J. DOUMATE, L. LEADI, L. R. TOYOU: Strictly or Semitrivial Principal Eigensurface for (p, q)-biharmonicSystems. Advances in Mathematical Physics Volume 2022, Article ID8751037, 11 pages.

P. DR ´ABEK AND M. ˆOTANI: Global bifurcation result for the p-biharmonic operator. Electron. J. Differential Equations 2001, no. 48, pp. 1-19.

A. EL KHALIL, S. KELLATI AND A. TOUZANI: On the spectrum of the p-biharmonic operator. In: 2002-Fez Conference on Partial Differential Equations, Electron. J. Differential Equations, Conference 09 (2002), 161-170.

D. GILBARG AND N. S. TRUDINGER: Elliptic Partial Differential Equations of Second Order. 2nd ed., Springer, New York, 1983.

K. BEN HADDOUCH, N. TSOULI AND Z. EL ALLALI: The Third Order Spectrum of p-Biharmonic Operator with Weight. Applicationes Mathematicae, 41, 2-3 (2014), pp.247-255.

K. BEN HADDOUCH, N. TSOULI, EL MILOUD HSSINI AND Z. EL ALLALI: On the First Eigensurface for the Third Order Spectrum of p-Biharmonic Operator with Weight. Applied Mathematical Sciences, Vol. 8, 2014, no. 89, 4413-4424.

EL M. HSSINI, M. MASSAR, N. TSOULI: Infinitely many solutions for the Navier boundary (p,q)-biharmonic systems. Electron. J. Differential Equations, Vol. 2012 (2012), No. 163, pp. 1-9.

L. LEADI, R. L. TOYOU: Principal Eigenvalue for Cooperative (p,q)-biharmonic Systems. J. Partial Diff. Eq., 32(2019) 33-51.

LIN LI, YU FU: Existence of Three Solutions for (p1, ..., pn)-biharmonic Systems. International Journal of Nonlinear Sciences, Vol. 10(2010) No. 4, pp. 495-506.

M. TALBI AND N. TSOULI: On the spectrum of the weighted p-biharmonic operator with weight. Mediterr. J. Math. 4 (2007), 73-86.