Singular elliptic problems with convection term in anisotropic media

الأصل · EN

We are concerned with singular elliptic problems of the form -Δu± p(d(x))g(u)= f(x,u)+μ|∇ u|ᵃ in Ω, where Ω is a smooth bounded domain in ⁿ, d(x)= dist(x,∂Ω), >0, μ∈, 0<a≤ 2, and f,k are nonnegative and nondecreasing functions. We assume that p(d(x)) is a positive weight with possible singular behavior on the boundary of Ω and that the nonlinearity g is unbounded around the origin. Taking into account the competition between the anisotropic potential p(d(x)), the convection term |∇ u|ᵃ, and the singular nonlinearity g, we establish various existence and nonexistence results.