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Quasilinear
Đề tài " Quasilinear and Hessian equations of Lane-Emden type " The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems: −∆p u = uq + µ, Fk [−u] = uq + µ, u ≥ 0, on Rn , or on a bounded domain Ω ⊂ Rn . Here ∆p is the p-Laplacian defined by ∆p u = div ( u| u|p−2 ), and Fk [u] is the k-Hessian defined as the sum of k × k principal minors of the Hessian matrix D2 u (k = 1, 2, . . . ,...
Liouville-type theorems for a quasilinear elliptic equation of the H´enon-typeIn the paper "Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type", We consider the H´enon-type quasilinear elliptic equation −Δmu = |x| aup where Δmu = div(|∇u| m−2∇u), m > 1, p>m − 1 and a ≥ 0. We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space RN . We prove the optimal Liouville-type theorem for dimension N
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