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A critical \(p\)-biharmonic system with negative exponents. (English) Zbl 1448.35182

Summary: In this paper, we are devoted to the study of critical \(p\)-biharmonic system with a parameter \(\lambda\), which involves strongly-coupled critical nonlinearities and negative exponents. We prove that there exists a positive constant \(\lambda_\ast\) such that the above problem admits at least two solutions if \(\lambda\in (0,\lambda_\ast)\).

MSC:

35J58 Boundary value problems for higher-order elliptic systems
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35J35 Variational methods for higher-order elliptic equations
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