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Marynets, K. (author), Pantova, D.H. (author)
We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the unique solution to the boundary value...
journal article 2022
document
Feckan, Michal (author), Marynets, K. (author)
We present original results in study of the second-order differential equation with exponential non-linearities, subjected to the Dirichlet boundary conditions. Using the proper substitution techniques, we reduce the given problem to the study of its lower and upper solutions.
journal article 2020
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Lindemulder, N. (author), Veraar, M.C. (author)
In this paper we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded H<sup>∞</sup>-calculus on weighted L<sup>p</sup>-spaces for power weights which fall outside the classical class of A<sub>p</sub>-weights. Furthermore, we characterize the domain of the operator and derive...
journal article 2020
document
Dall'Acqua, A. (author)
The main subject of this thesis concerns positivity for fourth order elliptic problems. By positivity we mean that a positive source term in the differential equation leads to a positive solution. For second order elliptic partial differential equations such a result is known and referred to by the name maximum principle. It is also well known...
doctoral thesis 2005
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