Dirichlet problems with singular and gradient quadratic lower order terms

An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term

In this paper we study a Dirichlet problem for an elliptic equation with degenerate coercivity and a singular lower order term with natural growth with respect to the gradient. The model problem is

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Dirichlet Problems with Singular Convection Terms and Applications to Some Elliptic Systems

To be more precise, in [2] is proved the existence of u { weak solution belonging to W 1,2 0 (Ω) ∩ L ∗∗ (Ω), if m ≥ 2N N+2 (“Stampacchia” theory); distributional solution belonging to W 1,m ∗ 0 (Ω), if 1 < m < 2N N+2 (“Calderon-Zygmund” theory); (5) where m∗ = mN N−m (1 ≤ m < N) and m ∗∗ = mN N−2m (1 ≤ m < N 2 ). Note that the above existence results are exactly the results proved with E = 0 in...

Title AN L^p-APPROACH TO SINGULAR LINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

The Dirichlet and Focal Boundary Value Problems for Higher Order Quasi-halflinear Singular Differential Equations

For higher order quasi-halflinear singular differential equations, the Dirichlet and focal boundary value problems are considered. Analogues of the Fredholm first theorem are proved and on the basis of these results optimal in some sense sufficient conditions of solvability of the above-mentioned problems are found. îâäæñéâ. éŽôŽèæ îæàæï çãŽäæ êŽýâãîŽáûîòæãæ ïæêàñèŽîñèæ áæòâîâêùæŽèñîæ àŽêðëèâIJ...