On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations.
On the Chaplighin method for partial differential equations of the first order
On the characteristics for a system of partial differential equations of the first order in a special case
On the circle criterion for boundary control systems in factor form : Lyapunov stability and Lur’e equations
A Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur’e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on results...
On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations
A Lur'e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur'e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on...
On the continuation of solutions for elliptic equations in two variables
On the continuity of heat potentials
On the convergence of numerical schemes for the Boltzmann equation
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 Dirac delta as initial condition for nonlinear Schrödinger equations
On the Dirichlet problem for a second order elliptic system with degeneration on the entire domain boundary.
On the elliptic problems involving multisingular inverse square potentials and concave-convex nonlinearities.
On the exact WKB analysis of microdifferential operators of WKB type
We first introduce the notion of microdifferential operators of WKB type and then develop their exact WKB analysis using microlocal analysis; a recursive way of constructing a WKB solution for such an operator is given through the symbol calculus of microdifferential operators, and their local structure near their turning points is discussed by a Weierstrass-type division theorem for such operators. A detailed study of the Berk-Book equation is given in Appendix.
On the existence and uniqueness of solutions of some partial differential functional equations
On the existence and uniqueness of solutions of the Darboux problem for partial differential-functional equations in a Banach space
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 nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method
The existence of nontrivial solutions is considered for the fractional Schrödinger-Poisson system with double quasi-linear terms: where is the fractional Laplacian for , with and . Under assumptions on and , we prove the existence of positive solutions and negative solutions for the above system by using perturbation method and the mountain pass theorem.
On the existence of the solution of Burger's equation for .