On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.
On maximum principles and Liouville theorems for quasilinear elliptic equations and systems
On mean value properties involving a logarithm-type weight
Two new assertions characterizing analytically disks in the Euclidean plane are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.
On minima of variational problems with some nonconvex constraints.
On minimizers with prescribed divergence
On minimizing noncoercive functionals on weakly vlosed sets
We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. The functionals considered belong to a class which includes semi-coercive, compact-coercive and P-coercive functionals. Some applications to nonlinear partial differential equations are given.
On Mixed Finite Element Methods for First Order Elliptic Systems.
On mixed finite element techniques for elliptic problems.
On monotone and Schwarz alternating methods for nonlinear elliptic PDEs
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On monotone-like mappings in Orlicz-Sobolev spaces
We study the mappings of monotone type in Orlicz-Sobolev spaces. We introduce a new class as a generalization of and extend the definition of quasimonotone map. We also prove existence results for equations involving monotone-like mappings.
On multi-lump solutions to the non-linear Schrödinger equation.
On multi-parameter error expansions in finite difference methods for linear Dirichlet problems
The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an (-dimensional) rectangular grid in the directions of the individual...
On multiple positive solutions of positone and non-positone problems.
On multiple solutions for nonhomogeneous system of elliptic equations.
On multiple solutions of concave and convex nonlinearities in elliptic equation on .
On multiple solutions of the Neumann problem involving the critical Sobolev exponent
We consider the Neumann problem involving the critical Sobolev exponent and a nonhomogeneous boundary condition. We establish the existence of two solutions. We use the method of sub- and supersolutions, a local minimization and the mountain-pass principle.
On multiply connected mesoscopic superconducting structures
On Neumann boundary value problems for elliptic equations
We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in , a is a weight function and f a nonlinear perturbation. Our approach is variational in character.
On Neumann boundary value problems for some quasilinear elliptic equations.