On a class of elliptic differential operators degenerating at one point
On a class of nonlocal problem involving a critical exponent
In this work, by using the Mountain Pass Theorem, we give a result on the existence of solutions concerning a class of nonlocal -Laplacian Dirichlet problems with a critical nonlinearity and small perturbation.
On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two
In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in . We prove that if the level lines of a solution have bounded curvature, then these level lines are straight lines. As a consequence, the solution is one-dimensional. The method also provides a result on free boundary problems of Serrin type.
On certain oscillatory properties for solutions of an equation with a biharmonic leading part
On ellipticity of fourth order opetaror
On existence in the Cauchy problem for the biharmonic equation
On nonoscillation of canonical or noncanonical disconjugate functional equations
Qualitative comparison of the nonoscillatory behavior of the equations and is sought by way of finding different nonoscillation criteria for the above equations. is a disconjugate operator of the form Both canonical and noncanonical forms of have been studied.
On some quasimetrics and their applications.
On the Convergence of the Conjugate Gradient Method for Singular Capacitance Matrix Equations from the Neumann Problem of the Poisson Equation.
On the Keldyš-Fichera boundary-value problem for degenerate quasilinear elliptic equations.
On the range of nonlinear operators with linear asymptotes which are not invertible
On the Regularity of the Solution of the Biharmonic Variational Inequality.
On the smoothness of the solutions to the elliptic systems
On the structure of layers for singularly perturbed equations in the case of unbounded energy
We consider singular perturbation variational problems depending on a small parameter . The right hand side is such that the energy does not remain bounded as . The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating...
On the structure of layers for singularly perturbed equations in the case of unbounded energy
We consider singular perturbation variational problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε → 0. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after...
Oscillation criteria for forced nonlinear elliptic equations of arbitrary order
Oб одной задаче Кона-Ниренберга.