Multiplicity Results for Degenerate Fractional p
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Li Wang
Abstract
In this paper, we deal with the existence of multiple nontrivial solutions for the following fractional
where parameter
The main feature and difficulty of our problems is the fact that the problem is degenerate.
Funding statement: The first author was supported by National Natural Science Foundation of China (11561024, 11701178), the second author was was supported by National Natural Science Foundation of China (11501186).
Acknowledgements
The authors would like to thank the referees for valuable comments and suggestions on improving this paper.
Competing interests The authors declare that they have no competing interests.
Authors contributions All authors contributed equally and significantly in writing this paper. All authors read and approved the final manuscript.
References
[1] Corréa F. J. S. A. and Figueiredo G. M., On a p-Kirchhoff equation via Krasnoselskii’S genus, Appl. Math. Lett. 22 (2009), 819–822.10.1016/j.aml.2008.06.042Suche in Google Scholar
[2] Dai G. and Liu D., Infinitely many positive solutions for a p(x)-Kirchhoff-type equation, J. Math. Anal. Appl. 359 (2009), 710–764.10.1016/j.jmaa.2009.06.012Suche in Google Scholar
[3] He X. and Zou W., Infinitely many positive solutions for Kirchhoff-type problems, Nonlinear Anal. 70 (2009), 1407–1414.10.1016/j.na.2008.02.021Suche in Google Scholar
[4] Jin J. and Wu X., Infinitely many radial solutions for Kirchhoff-type problems in ℝN, J. Math. Anal. Appl. 369 (2010), 564–574.10.1016/j.jmaa.2010.03.059Suche in Google Scholar
[5] Kirchhoff G., Mechanik, Teubner, Leipzig, 1883.Suche in Google Scholar
[6] Alves C. O., F. J. S. A. Corréa and T. F. Ma, Positive solutions for a quasilinear elliptic equation of Kirchhoff type, Comput. Math. Appl. 49 (2005), 85–93.10.1016/j.camwa.2005.01.008Suche in Google Scholar
[7] Fiscella A. and Valdinoci E., A critical Kirchhoff type problem involving a nonlocal operator, Nonlinear Anal. 94 (2014), 156–170.10.1016/j.na.2013.08.011Suche in Google Scholar
[8] Naimen D., Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent, Nonlinear Differ. Equ. Appl. 21 (2014), 885–914.10.1007/s00030-014-0271-4Suche in Google Scholar
[9] He Y., Li G. and Peng S., Concentrating bound states for Kirchhoff type problem involving critical Sobolev exponents, Adv. Nonlinear Stud. 14 (2014), 483–510.10.1515/ans-2014-0214Suche in Google Scholar
[10] Wang J., L. Tian, J. Xu and Zhang F., Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth, J. Differ. Equ. 253 (2012), 2314–2351.10.1016/j.jde.2012.05.023Suche in Google Scholar
[11] Brézis H. and Nirenberg L., Positive solutions of nonlinear elliptic problems involving critical Sobolev exponent, Comm. Pure Appl. Math. 36 (1983), 437–477.10.1002/cpa.3160360405Suche in Google Scholar
[12] Lions P. L., The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoam. 1 (1985), 145–201.10.4171/RMI/6Suche in Google Scholar
[13] Perera K., Squassina M. and Yang Y., Birfucation and multiplicity results for critical fractional p-Laplacian problems, Math. Nachr. 289 (2016), 332–342.10.1002/mana.201400259Suche in Google Scholar
[14] D’Ancona P. and Spagnolo S., Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math. 108} (1992), 247–262.10.1007/BF02100605Suche in Google Scholar
[15] Xiang M., Zhang B. and Ferrara M., Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian, J. Math. Anal. Appl. 424 (2015), 1021– 1041.10.1016/j.jmaa.2014.11.055Suche in Google Scholar
[16] Adams R., Spaces Sobolev, Press Academic, York New, 1975.Suche in Google Scholar
[17] Agarwal R., Perera K. and Zhang Z., On some nonlocal eigenvalue problems, Discrete Contin. Dyn. Syst. S 5 (2012), 707–714.10.3934/dcdss.2012.5.707Suche in Google Scholar
[18] Fadell E. and Rabinowitz P., Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math. 45 (1978), 139–174.10.1007/BF01390270Suche in Google Scholar
[19] Benci V., On critical point theory for indefinite functionals in the presence of symmetrics, Trans. Amer. Math. Soc. 274 (1982), 533–572.10.1090/S0002-9947-1982-0675067-XSuche in Google Scholar
[20] Perera K., Squassina M. and Yang Y., Bifurcation and multiplicity results for critical p-Laplacian problems, Topol. Methods Nonlinear Anal.47 (2016), 187–194.10.12775/TMNA.2015.093Suche in Google Scholar
[21] Xiang M., Zhang B. and Zhang X., A nonhomogeneous fractional p-Kirchhoff type problem involving critical exponent in ℝN, Adv. Stud Nonlinear. 17 (2017), 611–640.10.1515/ans-2016-6002Suche in Google Scholar
[22] Perera K., Agarwal R. P. and O’Regan D., Morse theoretic aspects of p-Laplacian type operators, volume 161 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2010.10.1090/surv/161Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Numerical Exploration of Heat Transfer and Lorentz Force Effects on the Flow of MHD Casson Fluid over an Upper Horizontal Surface of a Thermally Stratified Melting Surface of a Paraboloid of Revolution
- Ambient Vibration-Based System Identification of a Medieval Masonry Bastion for Health Assessment using Nonlinear Analyses
- Solvability of Anti-periodic BVPs for Impulsive Fractional Differential Systems Involving Caputo and Riemann–Liouville Fractional Derivatives
- Microcontroller Control/Synchronization of the Dynamics of Van der Pol Oscillators Submitted to Disturbances
- An Efficient Method for the Numerical Solution of a Class of Nonlinear Fractional Fredholm Integro-Differential Equations
- Radiant Heat Transfer in Nitrogen-Free Combustion Environments
- Variational Approaches to P(X)-Laplacian-Like Problems with Neumann Condition Originated from a Capillary Phenomena
- Global Mittag–Leffler Synchronization for Impulsive Fractional-Order Neural Networks with Delays
-
Multiplicity Results for Degenerate Fractional
- Numerical Investigation of the Wave-Front Tracking Algorithm for the Full Ultra-Relativistic Euler Equations
Artikel in diesem Heft
- Frontmatter
- Numerical Exploration of Heat Transfer and Lorentz Force Effects on the Flow of MHD Casson Fluid over an Upper Horizontal Surface of a Thermally Stratified Melting Surface of a Paraboloid of Revolution
- Ambient Vibration-Based System Identification of a Medieval Masonry Bastion for Health Assessment using Nonlinear Analyses
- Solvability of Anti-periodic BVPs for Impulsive Fractional Differential Systems Involving Caputo and Riemann–Liouville Fractional Derivatives
- Microcontroller Control/Synchronization of the Dynamics of Van der Pol Oscillators Submitted to Disturbances
- An Efficient Method for the Numerical Solution of a Class of Nonlinear Fractional Fredholm Integro-Differential Equations
- Radiant Heat Transfer in Nitrogen-Free Combustion Environments
- Variational Approaches to P(X)-Laplacian-Like Problems with Neumann Condition Originated from a Capillary Phenomena
- Global Mittag–Leffler Synchronization for Impulsive Fractional-Order Neural Networks with Delays
-
Multiplicity Results for Degenerate Fractional
- Numerical Investigation of the Wave-Front Tracking Algorithm for the Full Ultra-Relativistic Euler Equations
