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Steklov eigenvalue problem with a-harmonic solutions and variable exponents

  • Belhadj Karim , Abdellah Zerouali EMAIL logo and Omar Chakrone
Published/Copyright: February 5, 2020
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Abstract

Using the Ljusternik–Schnirelmann principle and a new variational technique, we prove that the following Steklov eigenvalue problem has infinitely many positive eigenvalue sequences:

{div(a(x,u))=0in Ω,a(x,u)ν=λm(x)|u|p(x)-2uon Ω,

where ΩN(N2) is a bounded domain of smooth boundary Ω and ν is the outward unit normal vector on Ω. The functions mL(Ω), p:Ω¯ and a:Ω¯×NN satisfy appropriate conditions.

Acknowledgements

We would like to thank the anonymous referee for valuable suggestions.

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Received: 2018-02-27
Revised: 2019-03-16
Accepted: 2019-04-16
Published Online: 2020-02-05
Published in Print: 2021-06-01

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