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Existence of Positive Solutions for Generalized Laplacian Problems with a Parameter

김찬균
영남수학회 (Youngnam Mathematical Society)|2022.01|East Asian Mathematical Journal|제38권 제1호|pp. 33-41

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참고문헌

키워드

positive solutionsingular weight functiongeneralized-Laplacian problem
주제분류수학

초록

In this paper, we study singular Dirichlet boundary value problems involving $\varphi$-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity $f=f(u)$ has a positive falling zero and is either superlinear or sublinear at $u=0$.

Abstract

In this paper, we study singular Dirichlet boundary value problems involving $\varphi$-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity $f=f(u)$ has a positive falling zero and is either superlinear or sublinear at $u=0$.

참고문헌 (18)

  1. R.P. Agarwal, "Eigenvalues and the one-dimensional p-Laplacian", J. Math. Anal. Appl, 266(2), pp.383~400 (2002)
  2. K. Deimling, "Nonlinear functional analysis" (1985), Springer-Verlag
  3. D. Guo, "Nonlinear problems in abstract cones" (1988), Academic Press, Inc
  4. J. Jeong, "Existence of positive solutions to singular boundary value problems involving ϕ-laplacian", Mathematics, 7(654), pp.1~13 (2019)
  5. J. Jeong, "Existence of positive solutions to singular ϕ-laplacian nonlocal boundary value problems when ϕ is a sup-multiplicative-like function", Mathematics, 8(420), pp.1~18 (2020)
  6. G. L. Karakostas, "Positive solutions for the Φ-Laplacian when Φ is a sup-multiplicative-like function", Electron. J. Differential Equations, (68), pp.1~12 (2004)
  7. G. L. Karakostas, "Triple positive solutions for the Φ-Laplacian when Φ is a sup-multiplicative-like function", Electron. J. Differential Equations, (69), pp.1~13 (2004)
  8. U. Kaufmann, "On one-dimensional superlinear indefinite problems involv-ing the φ-Laplacian", J. Fixed Point Theory Appl, 20(134), pp.1~9 (2018)
  9. U. Kaufmann, "Positive solutions for nonlinear problems involving the one-dimensional ϕ-Laplacian", J. Math. Anal. Appl, 461(1), pp.24~37 (2018)
  10. C.G. Kim, "Existence of positive solutions for singular boundary value problems involving the one-dimensional p-Laplacian", Nonlinear Anal, 70(12), pp.4259~4267 (2009)
  11. C.G. Kim, "Existence of positive solutions for multi-point boundary value problem with strong singularity", Acta Appl. Math, 112(1), pp.79~90 (2010)
  12. C.G. Kim, "Existence, nonexistence and multiplicity of positive solutions for singular boundary value problems involving ϕ-laplacian", Mathematics, 7(953), pp.1~12 (2019)
  13. E.K. Lee, "A multiplicity result for generalized Laplacian systems with multiparameters", Nonlinear Anal, 71(12), pp.366~376 (2009)
  14. 이용훈, "Multiplicity results of positive solutions for singular generalized Laplacian systems", 대한수학회지, 56(5), pp.1309~1331 (2019), 대한수학회[DOI]
  15. Y.H. Lee, "Existence and multiplicity results for generalized Laplacian problems with a parameter", Bull. Malays. Math. Sci. Soc, 43(1), pp.403~424 (2020)
  16. R. Shivaji, "A uniqueness result for a semipositone p-Laplacian problem on the exterior of a ball", J. Math. Anal. Appl, 445(1), pp.459~475 (2017)
  17. I. Sim, "On the existence of nodal solutions for singular one-dimensional φ-Laplacian problem with asymptotic condition", Commun. Pure Appl. Anal, 7(4), pp.905~923 (2008)
  18. H. Wang, "On the structure of positive radial solutions for quasilinear equations in an-nular domains", Adv. Differential Equations, 8(1), pp.111~128 (2003)

관련 논문AI추천

Existence and Multiplicity of Positive Solutions for Singular Generalized Laplacian Problems with a Parameter김찬균영남수학회 · East Asian Mathematical Journal2022 · 제38권 제5호EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS TO NONLOCAL BOUNDARY VALUE PROBLEMS WITH STRONG SINGULARITY김찬균영남수학회 · East Asian Mathematical Journal2023 · 제39권 제1호EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR p-LAPLACIAN PROBLEMS WITH A SINGULAR WEIGHT김찬균, 이용훈영남수학회 · East Asian Mathematical Journal2024 · 제40권 제1호Multiplicity results of positive solutions for singular generalized Laplacian systems이용훈, Xianghui Xu대한수학회 · 대한수학회지2019 · 제56권 제5호POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR p-LAPLACIAN WITH SIGN-CHANGING NONLINEAR TERMSWanyin Xu, Xiangfeng Li대한수학회 · 대한수학회보2010 · 제47권 제2호Positive solutions of singular Dirichlet problems via variational methodsJifeng Chu, Juntao Sun대한수학회 · 대한수학회지2013 · 제50권 제4호

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