A Remark on the Preceding paper of Fucik and Krbec.
A semilinear control problem involving homogenization.
A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential.
A sign-changing solution for a superlinear Dirichlet problem. II.
A singular equation with positive and free boundary solutions.
Para 0 < β < 1 consideramos la ecuación -Δu = χ{u > 0} (-u-β + λf(x, u)) en Ω con condición de borde tipo Dirichlet. Esta ecuación posee una solución maximal uλ ≥ 0 para todo λ > 0. Si λ es menor que una cierta constante λ*, uλ se anula en el interior del dominio creando una frontera libre, y para λ > λ* esta solución es positiva en Ω y estable. Establecemos la regularidad de uλ incluso en presencia de una frontera libre. Para λ ≥ λ* la solución del problema...
A singular ODE related to quasilinear elliptic equations.
A Singular Solution of the Capillary Equation. I. Existence.
A Singular Solution of the Capillary Equation. II. Uniqueness.
A solid-fluid model with unilateral contact conditions.
A spherical Harnack inequality for singular solutions of nonlinear elliptic equations
A stability result for -harmonic systems with discontinuous coefficients.
A strongly degenerate quasilinear equation : the elliptic case
We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation , where , , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes the case where , , being a convex function with linear growth as . In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the...
A strongly nonlinear problem arising in glaciology
The computation of glacier movements leads to a system of nonlinear partial differential equations. The existence and uniqueness of a weak solution is established by using the calculus of variations. A discretization by the finite element method is done. The solution of the discrete problem is proved to be convergent to the exact solution. A first simple numerical algorithm is proposed and its convergence numerically studied.
A supersolution-subsolution method for nonlinear biharmonic equations in
A symmetrization result for nonlinear elliptic equations.
We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W01,p (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.
A Variational Approach to Bifurcation in Lp on an Unbounded Symmetrical Domain.
A variational characterization of the Fucík spectrum and applications.
A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media
In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution of an elliptic equation, that we write , can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the method to...
About the Morse Theory for Certain Variational Problems.
Absence of local and global solutions to an elliptic system with time-fractional dynamical boundary conditions.