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This article presents suffcient conditions for the existence of solutions of the anisotropic quasilinear elliptic equation with variable exponent and nonlinear Robin boundary conditions, -ΣNi=1φ/φxi (|φu/φxi)NΣi=1|u|pi(x)-2u + λ|u|m(x)-2u = γg(x,u) in Ω NΣi=1|φu/φxi|pi(x)-2 φu/φxi vi = μ|u|q(x-2)u on ∂Ω Under appropriate assumptions on the data, we prove some existence and multiplicity results. The methods are based on Mountain Pass and Fountain theorems. [ABSTRACT FROM AUTHOR]

In this paper, we study existence, uniqueness and stability questions for the nonlinear parabolic equation: ∂u/∂t - Δpu + α(u) = f in ]0, T[xΩ, with Neumann-type boundary conditions and initial data in L¹. Our approach is based essentially on the time discretization technique by Euler forward scheme. [ABSTRACT FROM AUTHOR]

In this paper, we study a non-local initial boundary-value problem arising in Ohmic heating. By using a dynamical systems approach, some existence and uniqueness results are proved and the existence of a compact attractor is shown. [ABSTRACT FROM AUTHOR]