On the existence and smoothness of radially symmetric solutions of a BVP for a class of nonlinear, non-Lipschitz perturbations of the Laplace equation.
On the existence and the regularity of an initial boundary problem of vorticity equation
On the existence and the stability of solutions for higher-order semilinear Dirichlet problems
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.
On the Existence and Uniqueness of Non-homogeneous Motions in Exterior Domains.
On the existence and uniqueness of solutions of Darboux problem for partial differential-functional equations
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 and uniqueness of solutions of the Goursat problem for systems of functional partial differential equations of hyperbolic type.
On the existence for the Cauchy-Neumann problem for the Stokes system in the -framework
The existence for the Cauchy-Neumann problem for the Stokes system in a bounded domain is proved in a class such that the velocity belongs to , where r > 3. The proof is divided into three steps. First, the existence of solutions is proved in a half-space for vanishing initial data by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered....
On the existence for the Dirichlet problem for the compressible linearized Navier-Stokes system in the -framework
The existence of solutions to the Dirichlet problem for the compressible linearized Navier-Stokes system is proved in a class such that the velocity vector belongs to with r > 3. The proof is done in two steps. First the existence for local problems with constant coefficients is proved by applying the Fourier transform. Next by applying the regularizer technique the existence in a bounded domain is shown.
On the existence of a classical solution of a mixed boundary problem for a second order one-dimensional hyperbolic equation. II.
On the existence of a component-wise positive radially symmetric solution for a superlinear system.
On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition
For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent...
On the existence of a positive solution for a semilinear elliptic equation in the upper half space.
On the existence of a positive solution of semilinear elliptic equations in unbounded domains
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the existence of blowing-up solutions for a mean field equation
On the existence of bounded solutions of nonlinear elliptic systems.
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.