In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally, in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
The study focuses on privacy in online social networks. It presents an empirical analysis of youtubers, a group that has not yet been studied in the Czech social sciences. Using interpretive phenomenological analysis and in-depth interviews, we show that there is a typical ‘career’ trajectory that youtubers proceed along, whose structure is determined by experiences of breach of privacy and by mechanisms of reparation. These mechanisms and practices must be employed in order to resolve a fundamental tension between the demand for self-disclosure, arising out of confessional culture and the ideology of authenticity, and the parallel demand for retaining privacy. Breach of privacy is conceptualised as a violation of the equilibrium of its three constitutive elements: content, border, and context. Such situations are experienced as threats to the identity of the youtubers, who seek to avoid these threats by means of reparation practices, changes in how they perform privacy, and the use of what we call tools of controlled (in)accessibility. Unlike normative critiques that lament the loss of privacy on social networks, this article concludes that youtubers are highly competent guardians of their own performed privacy.