Large and entire large solution for a quasilinear problem

In this article we give the existence results for the quasilinear elliptic problem _Δpu=b(x)f(u)${\Delta }_{p}u=b\left(x\right)f\left(u\right)$ in Ω,u(x)→∞$\Omega ,u\left(x\right)\to \infty$ as x→∂Ω$x\to \partial \Omega$, where Ω⊆R^N$\Omega \subseteq {\mathbb{R}}^N$ is a domain.     

Existence results for a quasilinear elliptic problem with a gradient term via shooting method

The main purpose of our paper is to complete and improve a theorem of Dupaigne, Ghergu and Radulescu [Lane-Emden-Fowler equations with convection and singular potential, J. Math. Pures Appliquees (Journal de Liouville, 87(2007), 563-581).] showing the existence of solution for quasilinear elliptic equations where the nonlinearity depends on x, u and gradient term. The proofs combine O.D.E. techniques and shooting arguments. Previous developments require a monotonicity of the nonlinearity, while our main result is applied to a larger class of nonlinearities.     

Existence and uniqueness of solutions for the Lane, Emden and Fowler type problem

This paper deals with the existence and uniqueness of a positive solution to the semilinear elliptic equation of the Lane, Emden and Fowler type.     

A necessary and a sufficient condition for the existence of the positive radial solutions to Hessian equations and systems with weights

In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou(existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters,Volume 50, December 2015, Pages 48–55).