A class of optimal control problems for quasilinear elliptic equations is considered, where the coefficients of the elliptic differential operator depend on the state function. Firstand second-order optimality conditions are discussed for an associated control-constrained optimal control problem. Main emphasis is laid on second-order sufficient optimality conditions. To this aim, the regularity...

We prove maximum and comparison principles for weak distributional solutions of quasilinear, possibly singular or degenerate, elliptic differential inequalities in divergence form on complete Riemannian manifolds. A new definition of ellipticity for nonlinear operators on Riemannian manifolds is introduced, covering the standard important examples. As an application, uniqueness results for some...

In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −∆u = h(x)u in IR , where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.

Abstract In this paper, we study some results on the existence and multiplicity of solutions for a class nonlocal quasilinear elliptic systems. fact, prove precise intervals positive parameters such that problem admits multiple solutions. Our approach is based variational methods.

An analysis of the finite element heterogeneous multiscale method for a class of quasilinear elliptic homogenization problems of nonmonotone type is proposed. We obtain optimal convergence results for dimension d ≤ 3. Our results, which also take into account the microscale discretization, are valid for both simplicial and quadrilateral finite elements. Optimal a-priori error estimates are obta...

A new mixed formulation recently proposed for linear problems is extended to quasilinear second order elliptic problems This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated i e the scalar unknown its gradient and its ux the coe cients times the gradient Based on this formulation mixed nite element approximations of the quasilinear ...

In oil production it is crucial to find out properties of the ground from various measurements of geophysical fields. In secondary oil recovery oil is extracted by pumping in water (through injecting wells) and creating pressure which pumps out oil through production wells. Water/oil pressure at wells is monitored providing with an information to determine two important characterictics of mediu...

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory. 2000 Mathematics Subject Classification: 35J60, 35J62, 35J70.

In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami (PS) condition.