Existence of multiple solutions for quasilinear systems via fibering method

By Y. Bozhkov, Enzo Mitidieri. 2003

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The Nehari manifold for systems of nonlinear elliptic equations (2006, background): “For the nonlinear elliptic systems, we refer to [2, 3, 6, 8, 11, 14, 20, 21] and to the survey article [13].”
A fibering map approach to a potential operator equation and its applications (2009, background): “, quasilinear boundary value problems (see [1, 2, 4, 7, 8, 10, 11, 13, 17]), problems with nonlinear boundary conditions (see [6, 12, 16]) and quasilinear elliptic systems (see [3, 5, 18]).”
Positive solutions for a weakly coupled nonlinear Schrödinger system (2006, background): “moreover, by Pohozaev identity (see [10,20] for the scalar case and [12] for the case of systems or see Proposition 5.”
The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions (2008, methodology): “For more similar problems, we refer the reader to Ahammou [1], Alves–de Morais Filho–Souto [5], Bozhkov–Mitidieri [6], Clément–de Figueiredo–Mitidieri [7], de Figueiredo–Felmer [8], EL Hamidi [11], Squassina [13] and Vélin [15], etc.”
Combined effects in nonlinear problems arising in the study of anisotropic continuous media (2016, methodology): “We also refer to Bozhkov and Mitidieri [8, 9] for relatively closed “convex-concave” settings, both for nonlinear differential equations and for quasilinear elliptic systems with Dirichlet boundary condition.”