For the homogeneous Dirichlet problem involving a system of equations driven by (p, q)-Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.
Motreanu, D., Vetro, C., Vetro, F. (2017). Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 11(2), 309-321 [10.3934/dcdss.2018017].
Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method
Motreanu, Dumitru;Vetro, Calogero;Vetro, Francesca
2017-01-01
Abstract
For the homogeneous Dirichlet problem involving a system of equations driven by (p, q)-Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.
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