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

Multiple solutions for a modified quasilinear Schrödinger elliptic equation with a nonsquare diffusion term

In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables

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

Existence of positive solutions for third-order semipositone boundary value problems on time scales

In this paper, we consider the existence of positive solutions for a semipositone third-order nonlinear ordinary differential equation on time scales. In suitable growth conditions, by considering the properties on time scales and establishing a special cone, some new results on the existence of positive solutions are established when the nonlinearity is semipositone