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Nontrivial Solutions to Boundary Value Problems for Semilinear Δγ-Differential Equations


Duong Trong Luyen

Source title: 
Applications of Mathematics, 2021 (ISI)
Academic year of acceptance: 

In this article, we study the existence of nontrivial weak solutions for the following boundary value problem:

−Δγu = f(x, u) in Ω, u = 0 on Ω,

where Ω is a bounded domain with smooth boundary in a, Ω ∩ {xj = 0} ≠ ∅ for some j, Δγ is a subelliptic linear operator of the type


where γ(x) = (γ1(x), γ2(x), …, γN(x)) satisfies certain homogeneity conditions and degenerates at the coordinate hyperplanes and the nonlinearity f(x, ξ) is of subcritical growth and does not satisfy the Ambrosetti-Rabinowitz (AR) condition.