Results in Mathematics

, 74:67 | Cite as

Existence and Multiplicity of Solutions for p-Laplacian Neumann Problems

  • Qin Jiang
  • Sheng Ma
  • Daniel PaşcaEmail author


In this paper, existence theorems are proved for p-Laplacian Neumann problems under the Landesman–Lazer type condition. Our results are derived from a classical saddle point theorem and the least action principle respectively. Furthermore, multiplicity of solutions is established by applying a known multiple critical points result due to H. Brezis and L. Nirenberg. The above-mentioned conclusions are based on variational methods.


Neumann problem p-Laplacian critical point saddle point theorem Landesman–Lazer type condition 

Mathematics Subject Classification

35J50 49J35 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsHuanggang Normal UniversityHubeiChina
  2. 2.Department of Mathematics and InformaticsUniversity of OradeaOradeaRomania

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