Nontrivial Solutions to Boundary Value Problems for Semilinear Δγ-Differential Equations
Nontrivial Solutions to Boundary Value Problems for Semilinear Δγ-Differential Equations
Source title:
Applications of Mathematics,
2021
(ISI)
Academic year of acceptance:
2020-2021
Abstract:
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 , 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.