On the Existence of Three Solutions for Some Classes of Two-Point Semi-linear and Quasi-linear Differential Equations

Abstract

A general theorem concerning the three critical points for some classes of coercive functionals depending on a real parameter is established, which may derive existence’s results of three solutions with various sufficient conditions for some classes of two-point semi-linear boundary value problems. Moreover, by applying known three existence theorems, we derive multiple existence results for a class of quasi-linear differential equation.

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Correspondence to Somayeh Saiedinezhad.

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Communicated by Asadollah Aghajani.

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Saiedinezhad, S. On the Existence of Three Solutions for Some Classes of Two-Point Semi-linear and Quasi-linear Differential Equations. Bull. Iran. Math. Soc. 46, 1243–1255 (2020). https://doi.org/10.1007/s41980-019-00323-2

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Keywords

  • Critical points
  • Three solutions
  • Two-point boundary value problem
  • Eigenvalue problem

Mathematics Subject Classification

  • 34B09
  • 58E05