Asymptotic stability results for certain integral equations.
Asymptotically almost periodic and almost periodic solutions for a class of evolution equations.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Boundary value problems for differential equations with deviating arguments
Boundary-value problems for second-order differential operators with nonlocal boundary conditions.
Bourgin–Yang-type theorem for -compact perturbations of closed operators. I: The case of index theories with dimension property.
asymptotic equivalence for some functional equation of Volterra type.
Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces
In this paper, we present the existence result for Carathéodory type solutions for the nonlinear Sturm- Liouville boundary value problem (SLBVP) in Banach spaces on an arbitrary time scale. For this purpose, we introduce an equivalent integral operator to the SLBVP by means of Green’s function on an appropriate set. By imposing the regularity conditions expressed in terms of Kuratowski measure of noncompactness, we prove the existence of the fixed points of the equivalent integral operator. Mönch’s...
Cauchy problems in weighted Lebesgue spaces
Global solvability and asymptotics of semilinear parabolic Cauchy problems in are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over , . In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.
Coerciveness inequality for nonlocal boundary value problems for second order abstract elliptic differential equations.
Compact imbeddings in weighted Sobolev spaces and nonlinear boundary value problems
Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion
Let denote the generator of the rotation group in the space , where denotes the unit circle. We show that the stochastic Cauchy problem where is a standard Brownian motion and is fixed, has a weak solution if and only if the stochastic convolution process has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all...
Convergence estimate for second order Cauchy problems with a small parameter
We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
Convergence for hyperbolic singular perturbation of integrodifferential equations.
Convex solutions of systems arising from Monge-Ampère equations.
Correction to the paper: Random coincidence degree theory with applications to random differential inclusions
Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity
This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation , by means of regularly varying functions, where is a positive constant and is a positive continuous function on . It is shown that if is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to as and to acquire...
Derivative of the norm of a linear mapping and its application to differential equations
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
Differential inclusions and multivalued integrals
In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented...