A class of nonlinear elliptic systems with Steklov-Neumann nonlinear boundary conditions

The sub-supersolution method for variable exponent double phase systems with nonlinear boundary conditions

“…For systems with convection terms only few works are available: we mention the papers of Guarnotta-Marano [24,25], Guarnotta-Marano-Moussaoui [27] and Faria-Miyagaki-Pereira [18]. Neumann systems without gradient dependence on the nonlinearity can be found in Chabrowski [7] and de Godoi-Miyagaki-Rodrigues [11]. Finally, we mention some works pertaining equations exhibiting convection terms and subjected to Dirichlet or Neumann boundary conditions: we refer to Averna-Motreanu-Tornatore [1], de Araujo-Faria [10], Dupaigne-Ghergu-Rȃdulescu [13], El Manouni-Marino-Winkert [14], Faraci-Motreanu-Puglisi [16], Faraci-Puglisi [17], Figueiredo-Madeira [19], Gasiński-Papageorgiou [22], Gasiński-Winkert [23], Guarnotta-Marano-Motreanu [26], Liu-Motreanu-Zeng [30], Marano-Winkert [31], Motreanu-Tornatore [33], Motreanu-Winkert [34], Papageorgiou-Rȃdulescu-Repovš [35], and Vetro-Winkert [37].…”

Nonzero positive solutions of a multi-parameter elliptic system with functional BCs

“…where ĥ is a continuous function. In the context of radial solutions of PDEs on annular domains, conditions similar to (1.5) have been investigated recently in [5,7,8,9,10]. We stress that nonlinear BCs have been widely studied for different classes of differential equations, nonlinearities and domains, we refer the reader to [2,3,5,11,19,20,18,28] and references therein; in particular, the method of upper and lower solutions has been employed for the System (1.1) in the case of non-homogeneus (not necessarily constant) BCs in [2] and in the case of nonlinear BCs (when λ i = η i = 1) in [18,20].…”