On a certain Volterra-Fredholm type integral equation.
On a characterization of the Preisach model for hysteresis
On a class of parabolic integro-differential equations.
On a nonlinear compactness lemma in .
On a sub-supersolution method for the prescribed mean curvature problem
The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.
On a variational property of integral functionals and related conjectures
The aim of this paper is to give the proofs of those results that in [4] were only announced, and, at the same time, to propose some possible developments, indicating some of the most significant open problems.
On automatic boundedness of Nemytskiĭ set-valued operators
Let X, Y be two separable F-spaces. Let (Ω,Σ,μ) be a measure space with μ complete, non-atomic and σ-finite. Let be the Nemytskiĭ set-valued operator induced by a sup-measurable set-valued function . It is shown that if maps a modular space into subsets of a modular space , then is automatically modular bounded, i.e. for each set K ⊂ N(L(Ω,Σ,μ;X)) such that we have .
On characterization of the Lipschitzian composition operator between spaces of functions of bounded -variation
On continuous composition operators
Let I ⊂ ℝ be an interval, Y be a normed linear space and Z be a Banach space. We investigate the Banach space Lip₂(I,Z) of all functions ψ: I → Z such that , where [r,s,t;ψ]:= ((s-r)ψ(t)+(t-s)ψ(r)-(t-r)ψ(s))/((t-r)(t-s)(s-r)). We show that ψ ∈ Lip₂(I,Z) if and only if ψ is differentiable and its derivative ψ’ is Lipschitzian. Suppose the composition operator N generated by h: I × Y → Z, (Nφ)(t):= h(t,φ(t)), maps the set (I,Y) of all affine functions φ: I → Y into Lip₂(I,Z). We prove that if N is...
On Hammerstein equations with natural growth conditions.
On quadratic integral equations of Urysohn type in Fréchet spaces.
On some nonlinear potential problems.
On spaces and
On the autonomous Nemytskij operator in Hölder spaces.
On the compactness and condensing of nonlinear superposition operators
On the Conley index in Hilbert spaces in the absence of uniqueness
Consider the ordinary differential equation (1) ẋ = Lx + K(x) on an infinite-dimensional Hilbert space E, where L is a bounded linear operator on E which is assumed to be strongly indefinite and K: E → E is a completely continuous but not necessarily locally Lipschitzian map. Given any isolating neighborhood N relative to equation (1) we define a Conley-type index of N. This index is based on Galerkin approximation of equation (1) by finite-dimensional ODEs and extends...
On the existence of a fuzzy integral equation of Urysohn-Volterra type
We present an existence theorem for integral equations of Urysohn-Volterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.
On the existence of bounded continuous solution of Hammerstein integral equation
On the Hammerstein integral equations in Banach spaces
On the solutions of nonlinear initial-boundary value problems.