@article{Phuc2023, 
author = {Nguyen Cong Phuc and Igor E. Verbitsky},
title = {Uniqueness of entire solutions to quasilinear equations of    p-Laplace type},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {3},
pages = {1-33},
keywords = {quasilinear equations, p-Laplace, entire solutions, uniqueness of solutions, sub-natural growth},
url = {https://www.sciopen.com/article/10.3934/mine.2023068},
doi = {10.3934/mine.2023068},
abstract = {We prove the uniqueness property for a class of entire solutions to the equation         {                            −                      d            i            v                                          A                    (          x          ,          ∇          u          )          =          σ          ,                    u          ≥          0                                in                                              R                        n                    ,                                                                lim inf                                                |                                x                                  |                                →                ∞                                                        u          =          0          ,                        where    σ is a nonnegative locally finite measure in              R        n  , absolutely continuous with respect to the    p-capacity, and        d    i    v          A    (  x  ,  ∇  u  ) is the        A  -Laplace operator, under standard growth and monotonicity assumptions of order    p (   1  <  p  <  ∞) on        A    (  x  ,  ξ  ) (   x  ,  ξ  ∈            R        n  ); the model case        A    (  x  ,  ξ  )  =  ξ      |    ξ            |              p      −      2       corresponds to the    p-Laplace operator        Δ    p   on              R        n  . Our main results establish uniqueness of solutions to a similar problem,         {                            −                      d            i            v                                          A                    (          x          ,          ∇          u          )          =          σ                      u            q                    +          μ          ,                    u          ≥          0                                in                                              R                        n                    ,                                                                lim inf                                                |                                x                                  |                                →                ∞                                                        u          =          0          ,                        in the sub-natural growth case    0  <  q  <  p  −  1, where    μ  ,  σ are nonnegative locally finite measures in              R        n  , absolutely continuous with respect to the    p-capacity, and        A    (  x  ,  ξ  ) satisfies an additional homogeneity condition, which holds in particular for the    p-Laplace operator.}
}