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Resonant Steklov eigenvalue problem involving the (p, q)-Laplacian

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Abstract

In the present paper, we study the existence results of a positive solution for the Steklov eigenvalue problem driven by nonhomogeneous operator (p, q)-Laplacian with indefinite weights at resonance cases.

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References

  1. Anane, A., Chakrone, O., Moradi, N.: Regularity of the solutions to a nonlinear boundary problem with indenite weight. Bol. Soc. Paran. Mat. 29(1), 17–23 (2011)

    MATH  Google Scholar 

  2. Benouhiba, N., Belyacine, Z.: A class of eigenvalue problems for the \((p, q)\)-Laplacian in \(\mathbb{R}\). Int. Pure Appl. Math. 50, 727–737 (2012)

    Google Scholar 

  3. Benouhiba, N., Belyacine, Z.: On the solutions of \((p, q)\)-Laplacian problem at resonance. Nonlinear Anal. 77, 74–81 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cingolani, S., Degiovanni, M.: Nontrivial solutions for \(p\)-Laplace equations with right-hand side having p-linear growth at infinity. Commun. Partial Differ. Equ. 30, 1191–1203 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fǎrcǎseanu, M., Mihǎilescu, M., Stancu-Dumitru, D.: On the set of eigenvalues of some PDEs with homogeneous Neumann boundary condition. Nonlinear Anal. 116, 19–25 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Faria, L., Miyagaki, O., Motreanu, D.: Comparison and positive solutions for problems with \((P;Q)\)-Laplacian and convection term. Proc. Edinb. Math. Soc 57, 687–698 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bonder, J.Fernandez, Rossi, Julio D.: A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding. Publ. Mat. 46, 221–235 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Marano, S.A., Papageorgiou, N.S.: Constant-sign and nodal solutions of coercive \((p; q)\)-Laplacian problems. Nonlinear Anal. TMA 77, 118–129 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Mihǎilescu, M.: An eigenvalue problem possessing a continuous family of eigenvalues plus an isolated eigenvalue. Commun. Pure Appl. Anal. 10, 701–708 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Motreanu, D., Tanaka, M.: On a positive solution for (p; q)-Laplace equation with indeffinite weight. Min. Theory Appl. 1, 1–18 (2015)

    Google Scholar 

  11. Motreanu, D., Tanaka, M.: Generalized eigenvalue problems of non-homogeneous elliptic operators and their application. Pacif. J. Math. 265, 151–184 (2013)

    Article  MATH  Google Scholar 

  12. Ricceri, B.: Nonlinear eigenvalue problems. Handbook of Nonconvex Analysis and Applications, pp. 543–595. Int. Press, Somerville (2010)

  13. Sidiropoulos, N.E.: Existence of solutions to indefinite quasilinear elliptic problems of \(P\)-\(Q\)-Laplacian type. Elect. J. Differ. Equ. 2010(162), 1–23 (2010)

    MathSciNet  MATH  Google Scholar 

  14. Tanaka, M.: Generalized eigenvalue problems for \((p, q)\)-Laplace equation with indefinite weight. J. Math. Anal. Appl. 419(2), 1181–1192 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Vazquez, J.L.: A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12(3), 191–202 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yin, H., Yang, Z.: A class of p.q-Laplacian type equation with noncaveconvex nonlinearities in bounded domain. J. Math. Anal. Appl. 382, 843–855 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yin, H., Yang, Z.: Multiplicity of positive solutions to a \(p-q\)-Laplacian equations involving critical nonlinearity. Nonlinear Anal. TMA 75, 3021–3035 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zerouali, A., Karim, B.: Existence and non-existence of a positive solution for \((p,q)\)-Laplacian with singular weights. Bol. Soc. Paran. Mat. (3s.) v. 34 2, 147–167 (2016)

    MathSciNet  MATH  Google Scholar 

  19. Zerouali, A., Karim, B., Chakrone, O., Boukhsas, A.: On a positive solution for \((p,q)\)-Laplace equation with nonlinear boundary conditions and indefinite weights. Bol. Soc. Paran. Mat. (3s.) v. 38 4, 205–219 (2020)

    Google Scholar 

  20. Wu, M., Yang, Z.: A class of \(p\)-\(q\)-Laplacian type equation with potentials eigenvalue problem in \(\mathbb{R}^{N}\). Boundary Value Prob. 2009, 185319 (2009)

    Article  MATH  Google Scholar 

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Acknowledgements

The autors would like to thank the anonymous referee for valuable suggestions.

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Authors and Affiliations

  1. Centre Régional des Métiers de l’Éducation et de la Formation, Oujda, Maroc

    A. Zerouali

  2. Faculté des Sciences et Téchniques, Errachidia, Maroc

    B. Karim

  3. Faculté des Sciences, Oujda, Maroc

    O. Chakrone & A. Boukhsas

Authors
  1. A. Zerouali
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  2. B. Karim
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  3. O. Chakrone
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  4. A. Boukhsas
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Correspondence to A. Zerouali.

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Zerouali, A., Karim, B., Chakrone, O. et al. Resonant Steklov eigenvalue problem involving the (p, q)-Laplacian. Afr. Mat. 30, 171–179 (2019). https://doi.org/10.1007/s13370-018-0634-9

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  • DOI: https://doi.org/10.1007/s13370-018-0634-9

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