\`x^2+y_1+z_12^34\`
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Characterizing the existence of positive periodic solutions in the weighted periodic-parabolic degenerate logistic equation

  • * Corresponding author: David Aleja

    * Corresponding author: David Aleja 

This paper has been supported by the IMI of Complutense University and the Ministry of Science and Innovation of Spain under Grants PGC2018-097104-B-I00 and PID2021-123343NB-I00

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  • The main goal of this paper is to characterize the existence of positive periodic solutions for a general class of weighted periodic-parabolic logistic problems of degenerate type (see (1)). This result provides us with is an optimal substantial generalization of the previous findings of the authors in [1] and [2].

    Mathematics Subject Classification: 35K55, 35K57, 35B09, 35B10, 35Q92.

    Citation:

    \begin{equation} \\ \end{equation}
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  • Figure 1.  The graph of $ \Sigma(\lambda) $

  • [1] D. Aleja, I. Antón and J. López-Gómez, Solution components in a degenerate weighted BVP, Nonl. Anal., 192 (2020), 111690, 20 pp. doi: 10.1016/j.na.2019.111690.
    [2] D. Aleja, I. Antón and J. López-Gómez, Global structure of the periodic positive solutions for a general class of periodic-parabolic logistic equations with the indefinite weights, J. Math. Anal. Appl., 487 (2020), 123961, 23 pp. doi: 10.1016/j.jmaa.2020.123961.
    [3] H. Amann, Existence of multiple solutions for nonlinear elliptic boundary value problems, Indiana Univ. Math. J., 21 (1971-72), 925-935.  doi: 10.1512/iumj.1972.21.21074.
    [4] H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Diff. Eqns., 146 (1998), 336-374.  doi: 10.1006/jdeq.1998.3440.
    [5] I. Antón and J. López-Gómez, The strong maximum principle for periodic-parabolic systems and the existence of principal eigenvalues, in World Congress of Nonlinear Analysts 92's (Edited by L. Lakshmikantham), pp. 323–334, Walter de Gruyter, New York, 1996.
    [6] I. Antón and J. López-Gómez, Principal eigenvalues of weighted periodic-parabolic eigenvalue problems, Rend. Istit. Mat. Univ. Trieste, 49 (2017), 287-318. 
    [7] I. Antón and J. López-Gómez, Principal eigenvalue and maximum principle for cooperative periodic-parabolic systems, Nonl. Anal., 178 (2019), 152-189.  doi: 10.1016/j.na.2018.07.014.
    [8] A. Beltramo and P. Hess, On the principal eigenvalue of a periodic-parabolic operator, Comm. Partial Differential Equations, 9 (1984), 919-941.  doi: 10.1080/03605308408820351.
    [9] Y. Du and R. Peng, The periodic logistic equation with spatial and temporal degeneracies, Trans. Amer. Math. Soc., 364 (2012), 6039-6070.  doi: 10.1090/S0002-9947-2012-05590-5.
    [10] Y. Du and R. Peng, Sharp spatio-temporal patterns in the diffusive time-periodic logistic equation, J. Diff. Eqns., 254 (2013), 3794-3816.  doi: 10.1016/j.jde.2013.02.004.
    [11] P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Longman Scientifical and Technical, Essex, 1991.
    [12] J. López-Gómez, Linear Second Order Elliptic Operators, World Scientific Publishing, Hackensack, NJ, 2013. doi: 10.1142/8664.
    [13] J. López-GómezMetasolutions of Parabolic Problems in Population Dynamics, CRC Press, Boca Raton, 2016. 
    [14] J. López-Gómez, Protection zones in periodic-parabolic problems, Adv. Nonl. Stud., 20 (2020), 253-276.  doi: 10.1515/ans-2020-2084.
    [15] J. López-Gómez and M. Molina-Meyer, The maximum principle for cooperative weakly coupled elliptic systems and some applications, Diff. Int. Eqns., 7 (1994), 383-398. 
    [16] R. Peng and X.-Q. Zhao, Effect of diffusion and advention on the principal eigenvalue of a periodic-parabolic problem with applications, Calc. Var. Part. Diff. Eqns., 54 (2015), 1611-1642.  doi: 10.1007/s00526-015-0838-x.
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