On a global implicit function theorem for locally Lipschitz maps via nonsmooth critical point theory

We prove a non-smooth generalization of the global implicit function theorem. More precisely we use the non-smooth local implicit function theorem and the non-smooth critical point theory in order to prove a non-smooth global implicit function theorem for locally Lipschitz functions. A comparison between several global inversion theorems is discussed

Combined effects for non-autonomous singular biharmonic problems

We study the existence of nontrivial weak solutions for a class of generalized $p(x)$-biharmonic equations with singular nonlinearity and Navier boundary condition. The proofs combine variational and topological arguments. The approach developed in this paper allows for the treatment of several classes of singular biharmonic problems with variable growth arising in applied sciences, including the capillarity equation and the mean curvature problem

A Reflective Model to Stimulate Knowledge and Creativity in Teacher Education

AbstractThis paper discusses the importance of teaching the capacity to be reflective at earlier stages of the professional development, so that individuals can show readiness for learning throughout their career. It presents the case of 14 teacher trainees, whose use of reflective processes in relation to their understanding of professional identity and growth was investigated by means of a systematic enquiry method. Results showed that this approach can facilitate in-depth reflection, lead to autonomous learners that can make sense of the way old beliefs interfere with new theories and who are able to make the right decisions related to their learning for professional development

ASPECTS REGARDING THE FORMATION CHAINS SIZES TO SUBASSEMBLIES OF THE FIELD THE MECHANICS HEAVY

In this paper we present a case study on the construction and form a chain sizes for asubansamble of heavy mechanics. Importance training of chain size is reflected high quality for agriculturalmachineries and quality of grain. Dependence of the grain crushed and which not is crushed are in functionthe element closing chain size

Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactness

We study the following Kirchhoff equation $$- \left(1 + b \int_{\mathbb{R}^3} |\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u), \ x \in \mathbb{R}^3.$$ A special feature of this paper is that the nonlinearity $f$ and the potential $V$ are indefinite, hence sign-changing. Under some appropriate assumptions on $V$ and $f$, we prove the existence of two different solutions of the equation via the Ekeland variational principle and Mountain Pass Theorem

A Field Defining Study: Book review

Book Review: Cătălina Gheorghiu Iliescu, Un model polisistemic de analiză comparativă a textului dramatic din perspectiva traductologiei descriptive [A Polysistemic Model of Comparative Analysis of the Dramatic Text from the Perspective of Descriptive Translation Studies] (București: Editura Universității din București, 2018

Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential

We study perturbations of the eigenvalue problem for the negative Laplacian plus an indefinite and unbounded potential and Robin boundary condition. First we consider the case of a sublinear perturbation and then of a superlinear perturbation. For the first case we show that for $\lambda<\widehat{\lambda}_{1}$ ($\widehat{\lambda}_{1}$ being the principal eigenvalue) there is one positive solution which is unique under additional conditions on the perturbation term. For $\lambda\geq\widehat{\lambda}_{1}$ there are no positive solutions. In the superlinear case, for $\lambda<\widehat{\lambda}_{1}$ we have at least two positive solutions and for $\lambda\geq\widehat{\lambda}_{1}$ there are no positive solutions. For both cases we establish the existence of a minimal positive solution $\bar{u}_{\lambda}$ and we investigate the properties of the map $\lambda\mapsto\bar{u}_{\lambda}$