On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations.
On the convergence of the backward Euler algorithm for the multidimensional heat equation
The backward Euler algorithm for the multidimensional nonhomogeneous heat equation is analyzed, based on the finite element method. The existence and uniqueness of the numerical solution is investigated. Also, the convergence of the numerical solutions is studied.
On the definition and properties of p-superharmonic functions.
On the elliptic problems involving multisingular inverse square potentials and concave-convex nonlinearities.
On the existence of infinitely many periodic solutions for an equation of a rectangular thin plate
On the existence of multiple positive solutions for a certain class of elliptic problems
We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.
On the existence of the solution of Burger's equation for .
On the Ginzburg-Landau and related equations
We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture of the vortex...
On the Ginzburg–Landau model of a superconducting ball in a uniform field
On the ground states of vector nonlinear Schrödinger equations
On the rectifiability of domains with finite perimeter
On the singular limit in a phase field model of phase transitions
On the solution of boundary value problems for sandwich plates
A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.
On the solvability of a variational inequality problem and application to a problem of two membranes.
On the spectrum of the p-biharmonic operator involving p-Hardy's inequality
In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: in Ω, . By using the variational technique and the Hardy-Rellich inequality, we prove that the above problem has at least one increasing sequence of positive eigenvalues.
On the Stefan problem: the variational approach and some applications
On the variational principles for partial differential equations
On Two-Dimensional Quasi-Linear Elliptic Systems.
On Uniqueness of Boundary Values of Solutions of a Problem Arising in Plasma Physics.
On variational inequalities associated with the Navier-Stokes equation: Some bifurcation problems.