Sufficient conditions for the existence of heteroclinic solutions for -Laplacian differential equations

Abstract

In this paper, we consider the second-order discontinuous equation on the real line,

with an increasing homeomorphism such that and , with or for an -Carathéodory function and such that We point out that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the non-linearities and f. Moreover, as far as we know, this result is even new when that is, for the equation

Keywords:

• -Laplacian operator
• heteroclinic solutions
• problems on the real line
• fixed point theory

AMS Subject Classifications:

• 34B15
• 34B40
• 34C37
• 47H10

Acknowledgements

The author thanks the anonymous referees for their comments and remarks which improved this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by National Founds through FCT-Fundação para a Ciência e a Tecnologia as part of project : SFRH/BSAB/114246/2016.