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

Source abstract

In this article, we prove the Liouville‐type theorem for stable solutions of weighted p ‐Laplace–type Grushin equations urn:x-wiley:mma:media:mma5886:mma5886-math-0001 and urn:x-wiley:mma:media:mma5886:mma5886-math-0002 where p ≥ 2, q >0 and are nonnegative functions satisfying and as ‖ z ‖ G ≥ R 0 with p − N γ < b < θ + p , R 0 , C i ( i =1,2) are some positive constants. ∇ G =(∇ x ,(1+ γ )| x | γ ∇ y ), γ ≥ 0, and The results hold true for N γ < μ 0 ( p , b , θ ) in and q > q c ( p , N γ , b , θ ) in . Here, μ 0 and q c are new exponents, which are always larger than the classical critical ones and depend on the parameters p , b and θ . N γ = N 1 +(1+ γ ) N 2 is the homogeneous dimension of