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Three solutions to Dirichlet problems for second-order self-adjoint difference equations involving p-Laplacian

Feng Xiong,
Published: 1 April 2021
Advances in Difference Equations , Volume 2021, pp 1-15; doi:10.1186/s13662-021-03350-8

Abstract: This paper derives several sufficient conditions for the existence of three solutions to the Dirichlet problem for a second-order self-adjoint difference equation involving p-Laplacian through the critical point theory. Furthermore, by using the strong maximum principle, we prove that the three solutions are positive under appropriate assumptions on the nonlinearity. Finally, we present three examples to confirm our results.
Keywords: Three solutions / p-Laplacian / Self-adjoint / Boundary value problem / Critical point theory

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