Semilinear Robin problems driven by the Laplacian plus an indefinite potential

ABSTRACT

We study a semilinear Robin problem driven by the Laplacian plus an indefinite potential. We consider the case where the reaction term f is a Carathéodory function exhibiting linear growth near $\pm \mathrm{\infty }$. So, we establish the existence of at least two solutions, by using the Lyapunov-Schmidt reduction method together with variational tools.

COMMUNICATED BY:

• V. Radulescu

KEYWORDS:

• Semilinear Robin problem
• Carathéodory reaction
• indefinite potential
• Lyapunov-Schmidt reduction method

AMS SUBJECT CLASSIFICATIONS:

• 35J20
• 35J60

Acknowledgments

The author wishes to thank the editor and referees for their useful remarks.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

C. Vetro http://orcid.org/0000-0001-5836-6847