‎we study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{r}}^2$ with critical exponential growth‎. ‎this model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

In this paper, we consider the quasilinear elliptic equation in a smooth bounded domain. By using the method of lower and upper solutions, we study the existence, asymptotic behavior near the boundary and uniqueness of the positive blow-up solutions for quasilinear elliptic equation with nonlinear gradient term.

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Continuity results are given for the tra...

We provide conditions for the existence and uniqueness of positive solutions to the quasilinear elliptic system −∆pu = f(x, u, v) −∆qv = g(x, u, v) with Dirichlet boundary conditions on a bounded domain Ω ⊆ RN .

In this paper we establish existence and regularity of positive solutions for a singular quasilinear elliptic system with competitive structure. The approach is based on comparison properties, a priori estimates and the Schauder’s …xed point theorem.

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Continuity results are given for the tra...

We study existence and nonexistence of positive, spherically symmetric solutions of diagonal quasilinear elliptic systems involving equations with p-Laplacians, and with strong dependence on the gradient on the right-hand side. The existence proof is constructive, with solutions possessing explicit integral representation. Also, we obtain critical exponents of the gradient. We introduce the not...

In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.

Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in RN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations...