Liouville type theorems for stable solutions ofp-Laplace equation inRN

Liouville‐type theorem for nonlinear elliptic equations involving p‐Laplace–type Grushin operators

“…After that, the result in Wang and Ye was extended to problem with f ( u )= e u in Huang et al and equation −△ p u = f ( x ) g ( u ) in Chen et al, where g ( u )= e u or g ( u )=− u − q . Similar works on singular problems can be founded in other studies …”

“…However, as far as we know, the Liouville‐type theorem for the problem of with γ ≠0, p >2 and a ( z ), h ( z )≢1 has not been studied in the literature. Motivated by the above and the idea of other studies, in this paper, we are devoted to establish the Liouville property for the stable weak solutions of class to Equation.…”

“…Obviously, when γ =0, Equation becomes p ‐Laplace problem with the weighted power nonlinearity. So far, there have been many works dealing with the stable solutions of with γ =0 (see previous works and the references therein). The pioneering work in this direction is due to Farina; he proved that −△ u = e u has no stable classical solutions in for 2 ≤ N ≤ 9.…”

“…Although this work is motivated by the idea of previous works, it should be mentioned that the use of this technique in our case was by no means straightforward and required many nontrivial additional ideas.…”

Positive Solutions of Fractional Differential Equations with p-Laplacian

“…On the other hand, because of the wide mathematical and physical background, the existence of positive solutions for nonlinear integer-order boundary values problems with -Laplacian operator has received wide attention (see [8,12,13,21,[24][25][26][27][28][29]). For example, Su et al [28] considered the following four-point boundary values problems withLaplacian operator:…”