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Three solutions to discrete anisotropic problems with two parameters

100%
Galewski M., Kowalski P.
Open Mathematics
|
2014
|
tom 12
|
nr 10
1403-1415
EN
In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.
2
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On the completely indeterminate case for block Jacobi matrices

100%
Osipov A.
Concrete Operators
|
2017
|
tom 4
|
nr 1
48-57
EN
We consider the infinite Jacobi block matrices in the completely indeterminate case, i. e. such that the deficiency indices of the corresponding Jacobi operators are maximal. For such matrices, some criteria of complete indeterminacy are established. These criteria are similar to several known criteria of indeterminacy of the Hamburger moment problem in terms of the corresponding scalar Jacobi matrices and the related systems of orthogonal polynomials.
3
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On Popoviciu-Ionescu Functional Equation

100%
Almira J. M.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
5-15
EN
We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our solution is based on a generalization of Radó’s theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.
4
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Triple solutions for a Dirichlet boundary value problem involving a perturbed discretep(k)-Laplacian operator

84%
Khaleghi Moghadam M., Henderson J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1075-1089
EN
Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.
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