Study on a class of Schrödinger elliptic system involving a nonlinear operator

This paper considers a class of Schrödinger elliptic system involving a nonlinear operator. Firstly, under the simple condition on and ', we prove the existence of the entire positive bounded radial solutions. Secondly, by using the iterative technique and the method of contradiction, we prove the existence and nonexistence of the entire positive blow-up radial solutions. Our results extend the previous existence and nonexistence results for both the single equation and systems. In the end, we give two examples to illustrate our results

Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows

A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.&nbsp

The entire large solutions for a quasilinear Schrödinger elliptic equation by the dual approach

In this paper, we consider a Modified Nonlinear Schrödinger equation Δu−Δ(|u|2γ)|u|2γ−2u=q(x)F(u)Δu−Δ(|u|2γ)|u|2γ−2u=q(x)F(u) on View the MathML sourceRn(n≥3), where View the MathML sourceγ>12, qq is a nonnegative continuous function on View the MathML sourceRn, FF is a continuous positive and non-decreasing function on [0,∞)[0,∞). We establish sufficient conditions for the existence and nonexistence of positive entire large solutions for the given equation by using the dual approach