Existence of Two Non-zero Weak Solutions for a Nonlinear Navier Boundary Value Problem Involving the $p$-Biharmonic |
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Authors: | Bonanno Gabriele Chinn Antonia ORegan Donal |
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Institution: | 1.Department of Mathematics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Quang Binh, Vietnam ; |
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Abstract: | In this paper, we consider a class of non-cooperative elliptic systems of Kirchhoff type involving \(p\)-biharmonic operator and critical growth. With the help of the Limit index theory due to Li (Nonlinear Anal. TMA 30(7):4619–4627, 1997) and the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. |
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