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ANALYSIS OF L1-WEIGHTS IN ONE-DIMENSIONAL MINKOWSKI-CURVATURE PROBLEMS

  • Yang, Rui (Department of Mathematics, Pusan National University) ;
  • Lee, Yong-Hoon (Department of Mathematics, Pusan National University)
  • Received : 2018.12.03
  • Accepted : 2019.01.08
  • Published : 2019.01.31

Abstract

$L^1$-weight functions are investigated to give necessary conditions on the existence of nontrivial solutions for various types of scalar equations and systems of one-dimensional Minkowski-curvature problems.

Keywords

References

  1. A.M. Lyapunov, Probleme general de la stabilite du Mouvement, Ann. of Math. Stud. 17, Princeton Univ. Press, Princeton, NJ, USA, 1949.
  2. J.P. Pinasco, Lower bounds for eigenvalues of the one-dimensional p-Laplacian, Abstr. Appl. Anal., 2004 (2004) 147-153. https://doi.org/10.1155/S108533750431002X
  3. I. Sim and Y.H. Lee, Lyapunov inequalities for one-dimensional p-Laplacian problems with a singular weight function, J. Inequal. Appl., 2010 (2009) 1-9.
  4. I. Coelho, C. Corsato, F. Obersnel, and P. Omari, Positive solutions of the Dirichlet problem for one-dimensional Minkowski-curvature equation, Adv. Nonlinear Stud., 12 (2012) 621-638. https://doi.org/10.1515/ans-2012-0310
  5. R. Ma, H. Gao, and Y. Lu, Global structure of radial positive solutions for a prescribed mean curvature problem in a ball, J. Funct. Anal., 270 (2016) 2430-2455. https://doi.org/10.1016/j.jfa.2016.01.020
  6. G. Dai, Bifurcation and positive solutions for problem with mean curvature operator in Minkowski space, Calc. Var., 55 (2016) 1-17. https://doi.org/10.1007/s00526-015-0942-y
  7. K.J. Brown, C. Cosner, and J. Fleckinger, Principal eigenvalues for problems with indefinite weight function on ${\mathbb{R}}^N$, Proc. Amer. Math. Soc., 109 (1990) 147-155. https://doi.org/10.1090/S0002-9939-1990-1007489-1
  8. A. Constantin, A general-weighted Sturm-Liouville problem, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV, 24 (1998) 767-782.
  9. H. Asakawa, Nonresonant singular two-point boundary value problems, Nonlinear Anal., 44 (2001) 791-809. https://doi.org/10.1016/S0362-546X(99)00308-9
  10. G. Meng, P. Yan, and M. Zhang, Spectrum of One-Dimensional p-Laplacian with an inde nite integrable weight, Mediterr. J. Math., 7 (2010) 225-248. https://doi.org/10.1007/s00009-010-0040-5
  11. I. Sim, R. Kajikiya, and Y.H. Lee, On a criterion for discrete or continuous spectrum of p-Laplace eigenvalue problems with singular sign-changing weights, Nonlinear Anal., 72 (2010) 3515-3534. https://doi.org/10.1016/j.na.2009.12.034
  12. Y.H. Lee, eigenvalues of singular boundary value problems and existence results for positive radial solutions of semilinear elliptic problems in exterior domains, Differential and Integral Equations, 13 (2000) 631-648.
  13. Y.H. Lee and I. Sim, Global bifurcation phenomena for singular one-dimensional p-Laplacian, J. Differential Equations, 229 (2006) 229-256. https://doi.org/10.1016/j.jde.2006.03.021
  14. R. Ma and X. Han, Existence and multiplicity of positive solutions of a nonlinear eigenvalue problem with indefinite weight function, Appl. Math. Comput., 215 (2009) 1077-1083. https://doi.org/10.1016/j.amc.2009.06.042