EXISTENCE OF NONTRIVIAL NONNEGATIVE WEAK SOLUTIONS FOR A CLASS OF LOGISTIC-TYPE SYSTEMS
Main Article Content
Abstract
We consider logistic system
Assuming that the nonlinearities and satisfy certain growth conditions. We use the fixed point index theory and monotone minorants techniques to prove the existence of solutions for the system. This extends some known results.
Keywords
fixed point index, logistic system, (p-1) – sublinear
Article Details
References
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Drábek, P., & Hernández, J. (2001). Existence and uniqueness of positive solutions for some quasilinear elliptic problems. Nonlinear Analysis, 44(2), 189-204. https://doi.org/10.1016/S0362-546X(99)00258-8
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Lieberman, G. M. (1988). Boundary regularity solutions of degenerate elliptic equations. Nonlinear Analysis: Theory, Methods & Applications, 12(11), 1203-1219.
Papageorgiou, N. S., & Kyritsi-Yallourou, S. Th. (2009). Handbook of applied analysis. Springer.
Nguyen, B. H., & Bui, T. Q. (2017). Existence results for a class of logistic systems. Journal of Science, Ho Chi Minh City University of Education, 14(9), 5-14.
Nguyen, B. H., Bui, T. Q., & Nguyen, H. K. (2016). Existence and multiplicity results for generalized logistic equations. Nonlinear Analysis: Theory, Methods & Applications, 144, 77-92.
Yang, G. Y., & Wang, M. X. (2007). Structure of coexistence states for a class of quasilinear elliptic systems. Acta Mathematica Sinica, 23(9), 1649-1662.
Vázquez, J. L. (1984). A strong maximum principle for some quasilinear elliptic equations. Applied Mathematics and Optimization, 12(3), 191-202.
Díaz, J., Saà, E., & Brézis, H. (1987). Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires. Comptes Rendus de l'Académie des Sciences de Paris, Série I, 305, 521-524.
Drábek, P., & Hernández, J. (2001). Existence and uniqueness of positive solutions for some quasilinear elliptic problems. Nonlinear Analysis, 44(2), 189-204. https://doi.org/10.1016/S0362-546X(99)00258-8
Gasiński, L., & Papageorgiou, N. S. (2005). Nonlinear analysis. Chapman & Hall/CRC.
Iannizzotto, A., & Papageorgiou, N. S. (2011). Positive solutions for generalized nonlinear logistic equations of superdiffusive type. Topological Methods in Nonlinear Analysis, 38, 95-113.
Lieberman, G. M. (1988). Boundary regularity solutions of degenerate elliptic equations. Nonlinear Analysis: Theory, Methods & Applications, 12(11), 1203-1219.
Papageorgiou, N. S., & Kyritsi-Yallourou, S. Th. (2009). Handbook of applied analysis. Springer.
Nguyen, B. H., & Bui, T. Q. (2017). Existence results for a class of logistic systems. Journal of Science, Ho Chi Minh City University of Education, 14(9), 5-14.
Nguyen, B. H., Bui, T. Q., & Nguyen, H. K. (2016). Existence and multiplicity results for generalized logistic equations. Nonlinear Analysis: Theory, Methods & Applications, 144, 77-92.
Yang, G. Y., & Wang, M. X. (2007). Structure of coexistence states for a class of quasilinear elliptic systems. Acta Mathematica Sinica, 23(9), 1649-1662.
Vázquez, J. L. (1984). A strong maximum principle for some quasilinear elliptic equations. Applied Mathematics and Optimization, 12(3), 191-202.