On contact problems for nonlinear parabolic functional differential equations.
On strongly nonlinear elliptic equations with weak coercitivity condition.
We prove the existence and uniqueness of weak solutions of boundary problem value problems in an unbounded domain Ω ⊂ R for strongly nonlinear 2m order elliptic differential equations.
Semilinear hyperbolic functional equations
We consider second order semilinear hyperbolic functional differential equations where the lower order terms contain functional dependence on the unknown function. Existence and uniqueness of solutions for t ∈ (0,T), existence for t ∈ (0,∞) and some qualitative properties of the solutions in (0,∞) are shown.
On parabolic functional differential equations in unbounded domains
On some singular systems of parabolic functional equations
We will prove existence of weak solutions of a system, containing non-local terms , .
Second order quasilinear functional evolution equations
We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in (boundedness and stabilization as ) are shown.
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...
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