Abstract
In this paper, by using the Nehari manifold and variational methods, we study the existence of weak solutions for a class of \(\psi \)-Hilfer fractional Dirichlet boundary value problem with p-Laplacian and Hardy-type singularity term.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availibility statement
My manuscript has no associated data.
References
Sousa, J., Vanterler da C., and E. Capelas de Oliveira: On the \(\psi \)-Hilfer fractional derivative. Commun. Nonlinear Sci. Numer. Simul. 60 (2018), 72-91
Almeida, R.: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simul. 44, 460–481 (2017)
Kilbas, A.A., Srivastava, H.M.: and J. Elsevier, J. Trujillo. Theory and applications of fractional differential equations (2006)
Frank, R.L., Seiringer, R.: Non-linear ground state representations and sharp Hardy inequalities. J. Funct. Anal. 255, 3407–3430 (2008)
Sousa, J., Vanterler da, C., Capelas de Oliveira, E.: On the stability of a hyperbolic fractional partial differential equation. Diff. Equ. Dyn. Sys. 1-22 (2019)
Sousa, J., Vanterler da, C., Jiabin Zuo, Donal O’Regan.: The Nehari manifold for a \(\psi \)-Hilfer fractional \(p\)-Laplacian. Applicable Anal. 1-31 (2021)
Sousa, J., da Vanterler, C.: Nehari manifold and bifurcation for a \(\psi \)-Hilfer fractional \(p\)-Laplacian. Math. Meth. Appl. Sci. (2021). https://doi.org/10.1002/mma.7296
Ezati, R., Nemat N.: Existence of solutions to a Kirchhoff \(\psi \)-Hilfer fractional \(p\)-Laplacian equations. Math. Meth. Appl. Sci. (2021) https://doi.org/10.1002/mma.7593
Sousa, J., Vanterler da, C., Leandro, S., Tavares César, E., Torres Ledesma.: A variational approach for a problem involving a \(\psi \)-Hilfer fractional operator. J. Appl. Anal. Comput. 11.3 , 1610-1630 (2021)
Sousa, J., Vanterler da C., César, T., Ledesma, M.P., Jiabin Z.: Nehari Manifold for Weighted Singular Fractional \(p\)-Laplace Equations. Bull. Braz. Math. Soc. 1-31 (2022)
Sousa, J., Vanterler da C., Aurora, M., Pulido, P., Capelas de Oliveira, E.: Existence and regularity of weak solutions for \(\psi \)-Hilfer fractional boundary value problem. Mediter. J. Math. 18.4, 1-15:(2021)
Ma, L.: On nonlocal Hénon type problems with the fractional Laplacian. Nonlinear Anal. 203, 112190 (2021)
Ma, L.: On the Poisson equation of \(p\)-Laplacian and the nonlinear Hardy-type problems. Zeitschrift für Angewandte Mathematik und Physik 72(1), 1–8 (2021)
Li, J., Ma, Li.: Extremals to new Gagliardo-Nirenberg inequality and ground states. Appl. Math. Lett. 120 107266 (2021)
Ma, L., Ning, S.: Existence, multiplicity, and stability results for positive solutions of non-linear \(p\)-Laplacian equations. Chin. Ann. Math. 25, 275–286 (2004)
Bartsch, T., Wang, Z.Q.: Existence and multiplicity results for some superlinear elliptic problems on \({\mathbb{R} }^{3}\). Commun. Partial Differ. Equ. 20(9–10), 1725–1741 (1995)
Damascelli, L., Pardo, R.: A priori estimates for some elliptic equations involving the \(p\)-Laplacian. Nonlinear Anal. Real World Appl. 41, 475–496 (2018)
Damascelli, L., Merchan, S., Montoro, L., Sciunzi, B.: Radial symmetry and applications for a problem involving the \(\Delta _{p}\) operator and critical nonlinearity in \({\mathbb{R} }^{N}\). Adv. Math. 265, 313–335 (2014)
Guo, Z.M., Ma, L.: Asymptotic behavior of positive solutions of some quasilinear elliptic problems. J. Lond. Math. Soc. 76(2), 419–437 (2007)
Acknowledgements
All authors’ contributions to this manuscript are the same. All authors read and approved the final manuscript. We are very grateful to the anonymous reviewers for their useful comments that led to improvement of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author(s) declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sousa, J.V.d.C., Nyamoradi, N. & Lamine, M. Nehari manifold and fractional Dirichlet boundary value problem. Anal.Math.Phys. 12, 143 (2022). https://doi.org/10.1007/s13324-022-00754-x
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13324-022-00754-x
Keywords
- Fractional Dirichlet boundary value problem
- p-Laplacian
- Hardy-type singularity
- Existence of weak solutions