Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2015
Volume
Vol. 35
Number
No. 6
Description
Journal Volume
Opuscula Mathematica
Vol. 35 (2015)
Projects
Pages
Articles
Continuous spectrum of Steklov nonhomogeneous elliptic problem
(2015) Allaoui, Mostafa
By applying two versions of the mountain pass theorem and Ekeland’s variational principle, we prove three different situations of the existence of solutions for the following Steklov problem: $\begin{aligned}\Delta_{p(x)} u&=|u|^{p(x)-2}u \phantom{\lambda} \quad\text{in}\;\Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}&= \lambda|u|^{q(x)-2}u \quad\text{on}\;\partial\Omega,\end{aligned}$, where $\Omega \subset \mathbb{R}^N$ is a bounded smooth domain and $p,q: \overline{\Omega}\rightarrow(1,+\infty)$ are continuous functions.
Inversion of the Riemann-Liouville operator and its dual using wavelets
(2015) Baccar, Cyrine; Hamadi, Nadia Ben; Herch, Hajer; Meherzi, Fatma
We define and study the generalized continuous wavelet transform associated with the Riemann-Liouville operator that we use to express the new inversion formulas of the Riemann-Liouville operator and its dual.
Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem
(2015) Klimczak, Liliana
We consider a nonlinear Neumann elliptic equation driven by a $p$-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.
On vertex stability of complete k-partite graphs
(2015) Nikodem, Mateusz
Let $H$ be any graph. We say that graph $G$ is $H$-stable if $G-u$ contains a subgraph isomorphic to $H$ for an arbitrary chosen $u\in V(G)$. We characterize all $H$-stable graphs of minimal size where $H$ is any complete $k$-partite graph. Thus, we generalize the results of Dudek and Żak regarding complete bipartite graphs.
On the quasilinear Cauchy problem for a hyperbolic functional differential equation
(2015) Puźniakowska-Gałuch, Elżbieta
The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.