Radial positive solutions for (p(x),q(x))-Laplacian systems
DOI:
https://doi.org/10.5269/bspm.51625Resumen
In this paper, we study the existence of radial positive solutions for nonvariational elliptic systems involving the p(x)-Laplacian operator, we show the existence of solutions using Leray-Schauder topological degree theory, sustained by Gidas-Spruck Blow-up technique.
Referencias
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2. Garcia-Huidobro, M., Manasevich, R.,Schmitt, K.; Some bifurcation results for a class of p-Laplacian like operators, Differential and Integral Equations 10, 51-66, (1997). https://doi.org/10.57262/die/1367846883
3. Garcia-Huidobro, M., Manasevich, R., Ubilla, P.; Existence of positive solutions for some Dirichlet problems with an asymptotically homogeneous operator, Electron. J. Diff. Equ.10, 1-22, (1995).
4. Gidas, B., Spruck, J.; A priori Bounds for Positive Solutions of Nonlinear Elliptic Equations, Comm. in PDE, 6(8), 883-901, (1981). https://doi.org/10.1080/03605308108820196
5. Clement, Ph., Manasevich, R., Mitidieri, E., Positive solutions for a quasilinear system via Blow up, Comm. Partial Differential Equations 18 (12), 2071-2106, (1993). https://doi.org/10.1080/00927879308824124
6. Djellit, A., Moussaoui, M., Tas, S., Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems, Electronic J. Diff. Eqns. 54, 1-10, (2010).
7. Djellit, A., Tas, S.; On some nonlinear elliptic systems, Nonlinear Analysis, 59, 695-706, (2004). https://doi.org/10.1016/S0362-546X(04)00279-2
8. do O, J. M. B., Solutions to perturbed eigenvalue problems of the p−Laplacian in RN , Eur. J. Differential Equations 11, 1-15, (1997).
9. Marcos do O, J., Lorca S., Ubilla P.: ' Three positive solutions for elliptic equations in a ball. Appl. Math. Lett. 18, 1163-1169, (2005). https://doi.org/10.1016/j.aml.2004.12.001
10. Souto, M. A. S.: A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems. Diff Int. Equ. 8(5), 1245-1258, (1995). https://doi.org/10.57262/die/1369056053
11. Yu, L. S., Nonlinear p-Laplacian problems on unbounded domains, Proc. Amer. Math. Soc. 115 (4), 1037-1045, (1992). https://doi.org/10.1090/S0002-9939-1992-1162957-9
12. Wei, L., Feng, Z.: Existence and nonexistence of solutions for quasilinear elliptic systems. Dyn. PDE. 10(1), 25-42, (2013). https://doi.org/10.4310/DPDE.2013.v10.n1.a2
13. Ahammou, A., Iskafi, K.: Singular radial positive solutions for nonlinear elliptic systems. Adv. Dyn. Syst. Appl. 4(1), 1-17, (2009).
2. Garcia-Huidobro, M., Manasevich, R.,Schmitt, K.; Some bifurcation results for a class of p-Laplacian like operators, Differential and Integral Equations 10, 51-66, (1997). https://doi.org/10.57262/die/1367846883
3. Garcia-Huidobro, M., Manasevich, R., Ubilla, P.; Existence of positive solutions for some Dirichlet problems with an asymptotically homogeneous operator, Electron. J. Diff. Equ.10, 1-22, (1995).
4. Gidas, B., Spruck, J.; A priori Bounds for Positive Solutions of Nonlinear Elliptic Equations, Comm. in PDE, 6(8), 883-901, (1981). https://doi.org/10.1080/03605308108820196
5. Clement, Ph., Manasevich, R., Mitidieri, E., Positive solutions for a quasilinear system via Blow up, Comm. Partial Differential Equations 18 (12), 2071-2106, (1993). https://doi.org/10.1080/00927879308824124
6. Djellit, A., Moussaoui, M., Tas, S., Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems, Electronic J. Diff. Eqns. 54, 1-10, (2010).
7. Djellit, A., Tas, S.; On some nonlinear elliptic systems, Nonlinear Analysis, 59, 695-706, (2004). https://doi.org/10.1016/S0362-546X(04)00279-2
8. do O, J. M. B., Solutions to perturbed eigenvalue problems of the p−Laplacian in RN , Eur. J. Differential Equations 11, 1-15, (1997).
9. Marcos do O, J., Lorca S., Ubilla P.: ' Three positive solutions for elliptic equations in a ball. Appl. Math. Lett. 18, 1163-1169, (2005). https://doi.org/10.1016/j.aml.2004.12.001
10. Souto, M. A. S.: A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems. Diff Int. Equ. 8(5), 1245-1258, (1995). https://doi.org/10.57262/die/1369056053
11. Yu, L. S., Nonlinear p-Laplacian problems on unbounded domains, Proc. Amer. Math. Soc. 115 (4), 1037-1045, (1992). https://doi.org/10.1090/S0002-9939-1992-1162957-9
12. Wei, L., Feng, Z.: Existence and nonexistence of solutions for quasilinear elliptic systems. Dyn. PDE. 10(1), 25-42, (2013). https://doi.org/10.4310/DPDE.2013.v10.n1.a2
13. Ahammou, A., Iskafi, K.: Singular radial positive solutions for nonlinear elliptic systems. Adv. Dyn. Syst. Appl. 4(1), 1-17, (2009).
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2022-12-23
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