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Lingju Kong†
Abstract: We investigate weak solutions of a quasilinear (p, p)-biharmonic system with variational structure. Using the principal eigenvalue of the associated system and the linking theorem of Brezis and Nirenberg, we establish the existence of at least two nontrivial weak solutions for the eigenvalue parameter λ in a closed right neighborhood of zero. Our results apply in both resonant and nonresonant cases, depending on the asymptotic behavior of the nonlinear term. These findings extend earlier work on scalar biharmonic equations and systems, and cover several important special cases arising from different choices of the Keywords: biharmonic systems, principal eigenvalues, variational methods, weak solutions, linking theorem. MSC: 35P30, 35J48. DOI 10.56082/annalsarscimath.2026.1.81 †Lingju-Kong@utc.edu, Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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