Schéma aux différences finies pour une équation elliptique quasilinéaire dans un domaine arbitraire
We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an Ls-neighborhood of a reference function whereby the underlying analysis allows...
We deal with the boundary value problem where is an smooth bounded domain, is the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions on , and is bounded and continuous. Bifurcation theory is used as the right framework to show the existence of solution provided that satisfies certain conditions on the origin and at infinity.
In this paper, under the maximum angle condition, the finite element method is analyzed for nonlinear elliptic variational problem formulated in [4]. In [4] the analysis was done under the minimum angle condition.
We prove the existence of positive and of nodal solutions for , , where and , for a class of open subsets of lying between two infinite cylinders.
We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, , where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of lying between two infinite cylinders.