Minimax Theory and its Applications 07 (2022), No. 1, 109--118
Copyright Heldermann Verlag 2022
Multiple Weak Solutions of Biharmonic Systems
Lingju Kong
Dept. of Mathematics, University of Tennessee, Chattanooga, TN 37403, U.S.A.
Lingju-Kong@utc.edu
Roger Nichols
Dept. of Mathematics, University of Tennessee, Chattanooga, TN 37403, U.S.A.
Roger-Nichols@utc.edu
We obtain sufficient conditions for the existence of at least three weak solutions of a (p,q)-biharmonic system. We also consider the applications of our main theorem to some special cases of the system. The proof of our main theorem utilizes the variational approaches and a recent theorem of Ricceri on the existence of two global minima of a functional.
Keywords: Biharmonic system, principal eigenvalues, variational methods, multiple weak solutions.
MSC: 35P30, 35J48.
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