Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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EXISTENCE THEOREMS FOR CRITICAL DEGENERATE EQUATIONS INVOLVING THE GRUSHIN OPERATORS

  • Huong Thi Thu Nguyen (School of Applied Mathematics and Informatics Hanoi University of Science and Technology) ;
  • Tri Minh Nguyen (Institute of Mathematics Vietnam Academy of Science and Technology)
  • Received : 2022.02.05
  • Accepted : 2022.04.22
  • Published : 2023.01.31
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Abstract

In this paper we prove the existence of nontrivial weak solutions to the boundary value problem -G1u = u3 + f(x, y, u) in Ω, u ≥ 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain with smooth boundary in ℝ3, G1 is a Grushin type operator, and f(x, y, u) is a lower order perturbation of u3 with f(x, y, 0) = 0. The nonlinearity involved is of critical exponent, which differs from the existing results in [11, 12].

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Acknowledgement

The authors would like to thank the anonymous referees for their valuable comments and suggestions to improve the quality of the paper.

References

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