Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (5): 1788-1808.doi: 10.1007/s10473-021-0524-3

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Nikolaos S. PAPAGEORGIOU1, Nikolaos S. PAPAGEORGIOU2, Calogero VETRO3   

  1. 1. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece;
    2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy;
    3. 90123, Palermo, Italy
  • Received:2020-03-31 Revised:2021-04-10 Online:2021-10-25 Published:2021-10-21
  • Contact: Francesca VETRO

Abstract: We consider a nonlinear Dirichlet problem driven by a (p,q)-Laplace differential operator (1 < q < p). The reaction is (p-1)-linear near ±∞ and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q=2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

Key words: (p,q)-Laplacian, principal eigenvalue, constant sign and nodal solutions, extremal solutions, nonlinear regularity

CLC Number: 

  • 35J20