Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (4): 991-1000.doi: 10.1007/s10473-020-0408-y

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LANDESMAN-LAZER TYPE (p, q)-EQUATIONS WITH NEUMANN CONDITION

Nikolaos S. PAPAGEORGIOU1, Calogero VETRO2, Francesca VETRO3,4   

  1. 1. Department of Mathematics, National Technical University, Zografou campus, Athens 15780, Greece;
    2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy;
    3. Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam;
    4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • Received:2019-05-13 Revised:2019-10-17 Online:2020-08-25 Published:2020-08-21
  • Contact: Francesca VETRO E-mail:francescavetro@tdtu.edu.vn

Abstract: We consider a Neumann problem driven by the (p,q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.

Key words: Neumann problem, (p,q)-Laplacian, critical point, saddle point theorem, Landesman-Lazer type condition

CLC Number: 

  • 34B15
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