On the existence and regularity of vector solutions for quasilinear systems with linear coupling

2018/01/19 by Yong Ao, Jiaqi Wang, Ao, Yong +3
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1801.06307

Abstract

We study a class of linearly coupled system of quasilinear equations. Under some assumptions on the nonlinear terms, we establish some results about the existence and regularity of vector solutions for the p-Laplacian systems by using variational methods. In particular, we get two pairs of nontrivial solutions. We also study their different asymptotic behavior of solutions as the coupling parameter tends to zero.

Citations

• A relation between pointwise convergence of functions and convergence of functionals

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