A Landesman–Lazer Local Condition for Semilinear Elliptic Problems

  • M. C. M. Rezende
  • P. M. Sánchez-Aguilar
  • E. A. B. SilvaEmail author


The objective of this paper is to study the existence, multiplicity and non existence of solutions for semilinear elliptic problems under a local Landesman–Lazer condition. There is no growth restriction at infinity on the nonlinear term and it may change sign. In order to establish the existence of solution we combine the Lyapunov–Schmidt reduction method with truncation and approximation arguments via bootstrap methods. In our applications we also consider the existence of a bifurcation point which may have multiple positive solutions for a fixed value of the parameters.


Semilinear elliptic problems Variational methods Lyapunov–Schmidt reduction method Landesman–Lazer condition Bifurcation point 

Mathematics Subject Classification

35J20 35J61 58J55 



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© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasíliaBrazil
  2. 2.Faculdade de MatemáticaUniversidade Federal de Mato GrossoCuiabáBrazil

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