The convergence analysis and uniqueness of blow-up solutions for a Dirichlet problem of the general k-Hessian equations

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

“…http://www.journals.vu.lt/nonlinear-analysis Our main tool is analysis method and iterative technique as well as some suitable estimations. Here, in order to make the article more complete, we also recall some analysis methods and numerical techniques, which have been used to study various nonlinear ordinary differential equations and partial differential equations such as iterative methods [9,11,28,29,42,43,48,54,60,61,72,76,81,84,86], variational methods [17, 31-33, 36-39, 41, 46, 62, 67, 74, 78, 80, 83, 88, 89], fixed point theorems [13-15, 22, 23, 35, 47, 55, 57, 66, 70, 71, 73, 82], and upper and lower solution methods [58,68,69]. These theoretical methods and tools not only enrich the scientific field of differential equations, but also give some new scientific explanations and practical applications for the corresponding natural phenomena.…”

Existence and Uniqueness of Positive Solutions for Singular Nonlinear Fractional Differential Equation via Mixed Monotone Operator Method

“…From these paper, there have several results about existence of infinitely solutions, existence and nonexistence of blow-up solutions, existence and asymptotic properties of solutions or existence and nonexistence of entire large solutions. In [10][11][12], the authors considered existence of blow-up radial solutions of the k-hessian equations or convergence analysis and uniqueness of blow-up solutions of the k-hessian equations. Inspired by these conclusions,we realize that the questions about differential equations are very interesting and varied.…”

Existence and Nonexistence of Positive Solutions for High-Order Fractional Differential Equation Boundary Value Problems at Resonance

“…which implies that FBVP (1) happens to be at resonance. By virtue of the widespread applications, various differential equations have been studied by many researchers (see [1][2][3][4][5][6][7][8][9][10][11][12][13] and the references therein). Fractional-order models can describe many processes more accurately than integer-order models, and a great deal of papers focusing on FBVPs appeared in recent years (see [14][15][16][17][18][19][20][21][22][23]).…”