We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines sub and supersolution method with the pseudomonotone operator theory and perturbation arguments involving singular terms. 2000 Mathematics Subject Classi…cation: 35J50, 35J60, 35J75

We consider a prototype of quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of suband supersolutions on the basis of which we then develop the sub-supersolution method for variationalhemivariational inequalities. Furthermore, we give a...

We use the sub/supersolution method to analyze a semipositone Dirichlet problem for the p-Laplacian. To find a positive solution, we therefore focus on a related problem that produces positive subsolutions. We establish a new nonexistence result for this subsolution problem on general domains, discuss the existence of positive radial subsolutions on balls, and then apply our results to problems...

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing convection term. presence of the operator forces substantial change to functional setting previous works. existence location solutions through is established. abstract result applied find nontrivial, nonnegative bounded solutions.

Via a sub-supersolution method and a perturbation argument, we study the Lane-Emden-Fowler equation −∆u = p(x)[g(u) + f(u) + |∇u| ] in RN (N ≥ 3), where 0 < q < 1, p is a positive weight such that R∞ 0 rφ(r)dr < ∞, where φ(r) = max|x|=r p(x), r ≥ 0. Under the hypotheses that both g and f are sublinear, which include no monotonicity on the functions g(u), f(u), g(u)/u and f(u)/u, we show the exi...

We consider a portfolio optimization problem which is formulated as a stochastic control problem. Risky asset prices obey a logarithmic Brownian motion, and interest rates vary according to an ergodic Markov diffusion process. The goal is to choose optimal investment and consumption policies to maximize the infinite horizon expected discounted HARA utility of consumption. A dynamic programming ...