In this work we consider the existence of positive singular solutions style='text-indent:20px;'> \begin{document}$ \begin{equation} \left\{ \begin{array}{lcl} \hfill -\Delta u_1 & = \lambda_1 | \nabla u_2|^p \qquad \mbox{ in } \Omega, \\ u_2 \lambda_2 u_1|^q 0 on \partial \end{array}\right.\;\;\;\;\;\;\;(1) \end{equation} $\...

For 0 < p − 1 < q and either ǫ = 1 or ǫ = −1, we prove the existence of solutions of −∆pu = ǫu q in a cone CS , with vertex 0 and opening S, vanishing on ∂CS , under the form u(x) = |x|ω( x |x|). The problem reduces to a quasilinear elliptic equation on S and existence is based upon degree theory and homotopy methods. We also obtain a non-existence result in some critical case by an integral ty...

We consider the problem of non-existence of solutions for the following Hénon-Lane-Emden system  −∆u = |x|v in R , −∆v = |x|u in R , when pq > 1, p, q, a, b ≥ 0, and (p, q) are under the critical hyperbola, i.e. N+a p+1 + N+b q+1 > N − 2. We show that there is no positive bounded solution in dimension N = 3, extending a result established recently by Phan-Souplet in the scalar case. This solve...

A Newtonian-like theory inspired by the Brans–Dicke gravitational Lagrangian has been recently proposed us. For static configurations, coupling acquires an intrinsic spatial dependence within matter distribution. Therefore, interior of astrophysical configurations may provide a testable environment for this approach as long no screening mechanism is evoked. In work, we focus on stellar hydrosta...

In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of fact that Gravitational Decoupling allows decrease number degrees freedom once well known solution Einstein field is provided as seed so after demanding polytropic equation radial pressure system automatically closed. The not only extend both isotropic or ...

The gravitational lensing properties of cosmological halos depend upon the mass distribution within each halo. The description of halos as nonsingular, truncated isothermal spheres, a particular solution of the isothermal Lane-Emden equation (suitably modified for Λ 6= 0), has proved to be a useful approximation for the halos which form from realistic initial conditions in a CDM universe. We de...

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method could be proved are formulated and elaborated. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approximates the solution of a nonlinear differential equation by treating the nonlinear terms as a perturbation about the li...