If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological...
The original version of the article was published in Central European Journal of Mathematics, 2007, 5(1), 181–200, DOI: 10.2478/s11533-006-0036-3. Unfortunately, the original version of this article contains a mistake: in Theorem 5.2 only conditions (i) and (ii) (and not (iii)) are equivalent. We correct the theorem and its proof.
We study a class of hemivariational inequalities with p(x)-Laplacian. Applying nonsmooth critical point theory for locally Lipschitz functions, we obtain the existence of solutions on interior and exterior domains.
Let be a simple graph, let denote the degree of a vertex and let be a nonnegative integer function on with for each vertex . A -coloring of is an edge coloring such that for each vertex and each color , there are at least edges colored incident with . The -chromatic index of , denoted by , is the maximum number of colors such that a -coloring of exists. Any simple graph has the -chromatic index equal to or , where . A graph is nearly bipartite, if is not...
Based on the theory of variable exponent spaces, we study the regularity of local minimizers for a class of functionals with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain local Hölder continuity of minimizers.
We study the multiplicity of solutions for a class of p(x)-Laplacian equations involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going toward infinity.
This paper focuses on a new model called fuzzy exchange economy (FXE), which integrates fuzzy consumption, fuzzy initial endowment and the agent’s fuzzy preference (vague attitude) in the fuzzy consumption set. Also, the existence of the fuzzy competitive equilibrium for the FXE is verified through a related pure exchange economy. We define a core-like concept (called weak fuzzy core) of the FXE and prove that any fuzzy competitive allocation belongs to the weak fuzzy core. The fuzzy replica economy,...
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