The Dirichlet problem for discontinuous perturbations of the mean curvature operator in Minkowski space

Using the critical point theory for convex, lower semicontinuous perturbations of locally Lipschitz functionals, we prove the solvability of the discontinuous Dirichlet problem involving the operator $u\mapsto{div} (\frac{\nabla u}{\sqrt{1-|\nabla u|^2}})$.Comment: 8 page

The Dirichlet problem for discontinuous perturbations of the mean curvature operator in Minkowski space

Using the critical point theory for convex, lower semicontinuous perturbations of locally Lipschitz functionals, we prove the solvability of the discontinuous Dirichlet problem involving the operator u\mapsto\mbox{div} \Big(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\Big)

Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space

The first author is partially supported by a GENIL grant YTR-2011-7 (Spain) and by the grant PN-II-RU-TE-2011-3-0157 (Romania). The second author is partially supported by the grant PN-II-RU-TE-2011-3-0157 (Romania). The third author is partially supported by Ministerio de Economia y Competitividad, Spain, project MTM2011-23652.In this paper, by using Leray-Schauder degree arguments and critical point theory for convex, lower semicontinuous perturbations of C1-functionals, we obtain existence of classical positive radial solutions for Dirichlet problems of type div ( √1 − |∇ ∇v v|2 ) + f(|x|; v) = 0 in B(R); v = 0 on @B(R): Here, B(R) = {x ∈ RN : |x| < R} and f : [0; R] × [0; α) → R is a continuous function, which is positive on (0; R] × (0; α):GENIL (Spain) YTR-2011-7Ministerio de Economia y Competitividad, Spain MTM2011-23652PN-II-RU-TE-2011-3-015

Terapijska izmjena plazme i plazmafereza s dvostrukim filtriranjem u teškim neuroimunim bolestima

Therapeutic plasma exchange (TPE) is an extracorporeal blood purification technique, which removes large molecular weight particles such as autoantibodies from plasma. TPE is accepted by the American Society for Apheresis as first line treatment for some severe neuroimmune disorders. Double filtration plasmapheresis (DFPP) is a newer technique in which plasma is not entirely removed, only the antibodies, using special filters. High-dose intravenous immunoglobulins are an alternative treatment for these patients but are much more expensive. We reviewed medical records of 20 patients with severe neurological diseases requiring TPE or DFPP. We analyzed the indications, complications and efficacy of these procedures. After completing the procedures, neurological improvement was recorded in 80% of the patients, 5% had no improvement, and the mortality was 15%. The rate of neurological improvement was similar to other studies. None of the patients presented catheter related complications. Systemic complications were mild, transient and completely reversible.Terapijska izmjena plazme (TIP) je izvantjelesna tehnika pročišćavanja krvi kojom se iz plazme uklanjaju čestice velike molekularne težine poput autoantijela. Američko udruženje za aferezu prihvatilo je TIP kao liječenje prvog izbora za neke teške neuroimune bolesti. Plazmafereza s dvostrukim filtriranjem (PFDF) je nova tehnika kojom se ne uklanja sva plazma, nego samo antitijela, i to pomoću specijalnih filtara. Visoke doze intravenskih imunoglobulina su alternativna terapija za ove bolesnike, ali su znatno skuplji. Pregledali smo medicinske zapise 20 bolesnika s teškim neurološkim bolestima koji su trebali TIP ili PFDF. Analizirali smo indikacije, komplikacije i učinkovitost ovih postupaka. Nakon završetka postupaka poboljšanje neurološkog statusa zabilježeno je u 80% bolesnika, 5% ih nije imalo nikakvo poboljšanje, a smrtnost je bila 15%. Stopa neurološkog poboljšanja bila je slična onoj opisanoj u drugim istraživanjima. Komplikacije povezane s kateterom nisu zabilježene ni u jednog bolesnika. Sistemske komplikacije bile su blage, prolazne i u potpunosti reverzibilne

The Existence of solutions to nonlinear second order periodic boundary value problems

We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic solutions of some $\phi$-Laplacian type equations and Duffing type equations are investigated.Comment: 17 pages, to appear in Nonlinear Analysis Series A: Theory, Methods & Application

Periodic solutions for some phi-Laplacian and reflection equations

This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular initial and boundary value problems with reflection, which allows us to prove existence of solutions of the latter using the existence of the formerThe work was partially supported by FEDER and Ministerio de Economía y Competitividad, Spain, project MTM2013-43014-P. The second author was supported by FPU scholarship, Ministerio de Educación, Cultura y Deporte, Spain and Xunta de Galicia (Spain), project EM2014/032S