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

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