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Multiplicity results of positive solutions for singular generalized Laplacian systems

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초록

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^{1}$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at $0$ and $\infty$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

Abstract

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^{1}$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at $0$ and $\infty$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

참고문헌 (23)

  1. Ravi P. Agarwal, "Eigenvalues and the One-Dimensional p-Laplacian", Journal of Mathematical Analysis and Applications, 266(2), pp.383~400 (2002), Elsevier BV[DOI]
  2. R. P. Agarwal, "General existence principles for nonlocal boundary value problems with Φ-Laplacian and their applications", Abstr. Appl. Anal, 2006(30), pp.30~ (2006)[DOI]
  3. Ravi P. Agarwal, "Positive and dead core solutions of singular Dirichlet boundary value problems with Φ-Laplacian", Computers & Mathematics with Applications, 54(2), pp.255~266 (2007), Elsevier BV[DOI]
  4. Ravi P. Agarwal, "Dead cores of singular Dirichlet boundary value problems with ϕ-Laplacian", Applications of Mathematics, 53(4), pp.381~399 (2008), Institute of Mathematics, Czech Academy of Sciences[DOI]
  5. Dingyong Bai, "Three positive solutions for a generalized Laplacian boundary value problem with a parameter", Applied Mathematics and Computation, 219(9), pp.4782~4788 (2013), Elsevier BV[DOI]
  6. Xiyou Cheng, "Multiplicity of positive solutions for a -Laplacian system and its applications", Nonlinear Analysis: Real World Applications, 13(5), pp.2375~2390 (2012), Elsevier BV[DOI]
  7. K. Deimling, "Nonlinear Functional Analysis" (1985), Springer-Verlag
  8. J. I. Diaz, "Nonlinear partial di erential equations and free boundaries. Vol. I" (1985), Pitman (Advanced Publishing Program)
  9. João Marcos do Ó, "Positive radial solutions for some quasilinear elliptic systems in exterior domains", Communications on Pure & Applied Analysis, 5(3), pp.571~581 (2006), American Institute of Mathematical Sciences (AIMS)[DOI]
  10. P. Drabek, "Quasilinear elliptic equations with degenerations and singularities" (1997), Walter de Gruyter & Co
  11. Roland Glowinski, "Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology", ESAIM: Mathematical Modelling and Numerical Analysis, 37(1), pp.175~186 (2003), EDP Sciences[DOI]
  12. J. Henderson, "Nonlinear eigenvalue problems for quasilinear systems", Computers & Mathematics with Applications, 49(11-12), pp.1941~1949 (2005), Elsevier BV[DOI]
  13. M. A. Krasnoselskii, "Positive solutions of operator equations" (1964), P. Noordhoff Ltd
  14. Eun Kyoung Lee, "A multiplicity result for generalized Laplacian systems with multiparameters", Nonlinear Analysis: Theory, Methods & Applications, 71(12), pp.e366~e376 (2009), Elsevier BV[DOI]
  15. Yong-Hoon Lee, "Global Existence Structure of Parameters for Positive Solutions of a Singular $$(p_1,p_2)$$ ( p 1 , p 2 ) -Laplacian System", Bulletin of the Malaysian Mathematical Sciences Society, 42(3), pp.1143~1159 (2019), Springer Science and Business Media LLC[DOI]
  16. Donal O’Regan, "Some general existence principles and results for (ϕ(y;))' = qf(t, y, y'), 0 < t < 1", SIAM Journal on Mathematical Analysis, 24(3), pp.648~668 (1993), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  17. Donal O'Regan, "On the number of positive solutions of elliptic systems", Mathematische Nachrichten, 280(12), pp.1417~1430 (2007), Wiley[DOI]
  18. Justino Sánchez, "Multiple positive solutions of singular eigenvalue type problems involving the one-dimensional p-Laplacian", Journal of Mathematical Analysis and Applications, 292(2), pp.401~414 (2004), Elsevier BV[DOI]
  19. I. Sim, "A new solution operator of one-dimensional p-Laplacian with a sign-changing weight and its application", Abstr. Appl. Anal, 2012, pp.15~ (2012)[DOI]
  20. Haiyan Wang, "On the number of positive solutions of nonlinear systems", Journal of Mathematical Analysis and Applications, 281(1), pp.287~306 (2003), Elsevier BV[DOI]
  21. H. Wang, "On the structure of positive radial solutions for quasilinear equations in annular domains", Adv. Di erential Equations, 8(1), pp.111~128 (2003)
  22. X. Xu, "Some existence results of positive solutions for ϕ-Laplacian sys-tems", Abstr. Appl. Anal, 2014, pp.11~ (2014)[DOI]
  23. Xianghui Xu, "On singularly weighted generalized Laplacian systems and their applications", Advances in Nonlinear Analysis, 7(2), pp.149~165 (2018), Walter de Gruyter GmbH[DOI]

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