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Existence and asymptotic behavior of solutions for a class of Kirchhoff-type equations on the real half-line

Published 2025-07-07

  • Ishak Kettaf
    • ,
  • Sofiane Khoutir
    • ,
  • Hicham Kasri

Ishak Kettaf
University of Science and Technology Houari Boumediene

Sofiane Khoutir
University of Science and Technology Houari Boumediene

Hicham Kasri
University of Science and Technology Houari Boumediene

Abstract

This paper is concerned with the following Kirchhoff-type equation: -(a+b∫_0^(+∞)|u^' |^2 dx) u''+p(x)u=q(x)f(u),x∈(0,+∞), where a>0,b≥0 are constants, f∈C(R), p∈C(R^+,R_*^+) and q∈L^1 (0,∞). Firstly, by using the Ekeland's variational principle, we show the existence of solutions to the above equation in the case where f is a sublinear function. Then, we establish the existence of solutions in the case where f is a superlinear function by using the Mountain pass theorem. Moreover, we discuss the asymptotic behavior of the obtained solutions in both cases with respect to the parameter b. Some recent results are complemented and extended.

Keywords

Kirchhoff-type equation, sublinear, Ekeland's variational principle, superlinear, Mountain pass theorem, asymptotic behavior

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Author Biography

Ishak Kettaf

Departement of Mathematics, Ph.D. student

Sofiane Khoutir

Departement of Mathematics, Associate professor