본문 바로가기
KERD
논문KCI 등재

On a class of semilinear elliptic systems involving Grushin type operator

Nguyen Thanh Chung
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회논문집 (Communications of the KMS)|제29권 제1호|pp. 37-50

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

multiplicitynon-existencevariational methodssemilinear elliptic systemsGrushin type operator
주제분류수학

초록

Using variational methods, we prove some results on the non- existence and multiplicity of weak solutions for a class of semilinear elliptic systems of two equations involving Grushin type operators with sign- changing nonlinearities. We also shows that the similar results can be obtained for systems of m equations, where m is arbitrary.

Abstract

Using variational methods, we prove some results on the non- existence and multiplicity of weak solutions for a class of semilinear elliptic systems of two equations involving Grushin type operators with sign- changing nonlinearities. We also shows that the similar results can be obtained for systems of m equations, where m is arbitrary.

참고문헌 (26)

  1. A. Ambrosetti, "Dual variational methods in critical points theory and applications", J. Funct. Anal, 4, pp.349~381 (1973)
  2. L. Boccardo, "remarks on a system of quasilinear elliptic equations", Nonlinear Differential Equations Appl, 9(3), pp.309~323 (2002)
  3. J. F. Bonder, "Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities", Abstr. Appl. Anal, 2004(12), pp.1047~1056 (2004)
  4. N. M. Chuong, "Existence of solutions for a nonlinear degenerate elliptic system", Electron. J. Differential Equations, 2004(93), pp.1~15 (2004)
  5. N. M. Chuong, "Existence results for a semilinear parametric problem with Grushin type operator", Electron. J. Differential Equations, 2005(107), pp.1~12 (2005)
  6. F. Catrina, "On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existstence (and non existstence) and symmetry of extremal functions", Comm. Pure Appl. Math, 54(2), pp.229~258 (2001)
  7. N. T. Chung, "On a class of degenerate and singular elliptic systems in bounded domains", J. Math. Anal. Appl, 360(2), pp.422~431 (2009)
  8. R. Dautray, "Mathematical Analysis and Numerical Methods for Science and Technology I: Physical Origins and Classical Methods" (1985), Springer-Verlag
  9. V. Felli, "A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type", Adv. Nonlinear Stud, 3(4), pp.431~443 (2003)
  10. V. V. Grushin, "On a class of elliptic pseudo differential operators degenerate on a submanifold", Math. USSR Sbornik, 13, pp.155~183 (1971)
  11. L. Iturriaga, "Existence and multiplicity results for some quasilinear elliptic equation with weights", J. Math. Anal. Appl, 339(2), pp.1084~1102 (2008)
  12. T. D. Ke, "Existence of non-negative solutions for a semilinear degenerate elliptic system", Proceedings of the international conference on Abstract and Applied Analysis (Hanoi Aug. 2002) (2004), World Scientific
  13. T. T. Khanh, "On the analyticity of solutions to semilinear differential equations degenerated on a submanifold", J. Differential Equations, 249(10), pp.2440~2475 (2010)
  14. A. Kristaly, "Multiple solutions for a degenerate elliptic equation involving sublinear terms at infinity", J. Math. Anal. Appl, 352(1) (2009)
  15. F. Lascialfari, "Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator", Rend. Sem. Mat. Univ. Padova, 107, pp.139~152 (2002)
  16. M. Mihailescu, "Nonlinear eigenvalue problems for some degenerate elliptic operators on RN", Bull. Belg. Math. Soc. Simon Stevin, 12(3), pp.435~448 (2005)
  17. M. Mihailescu, "Equations involving a variable exponent Grushin-type operator", Nonlinearity, 24(10), pp.2663~2680 (2011)
  18. M. Mihailescu, "Ground state solutions of nonlinear singular Schrodinger equations with lack compactness", Math. Methods Appl. Sci, 26(11,), pp.897~906 (2003)
  19. M. K. V. Murthy, "Boundary value problems for some degenerate elliptic operators", Ann. Mat. Pura Appl, 80, pp.1~122 (1968)
  20. K. Perera, "Multiple positive solutions for a class of quasilinear elliptic boundary-value problems", Electron. J. Differential Equations, 2003(7), pp.1~5 (2003)
  21. V. Radulescu, "singular problems on infinite cones", Critical singular problems on infinite cones, Nonlinear Anal, 54(6), pp.1153~1164 (2003)
  22. N. T. C. Thuy, "Some existence and non-existence results for boundary value problems (BVP) for semilinear elliptic degenerate operators", Russ. J. Math. Phys, 9(3), pp.366~371 (2002)
  23. N. T. C. Thuy, "Nontrivial solutions to boundary value problems for semilinear strongly degenerate elliptic differential equations", Nonlinear Differential Equations Appl, 19(3), pp.279~298 (2012)
  24. N. M. Tri, "On Grushin's Equation", Matemachicheskie Zametki, 63, pp.95~105 (1988)
  25. N. M. Tri, "Critical Sobolev exponent for degenerate elliptic operators", Acta Math. Vietnamica, 23(1), pp.83~94 (1998)
  26. B. J. Xuan, "The eigenvalue problem of a singular quasilinear elliptic equation", Electron. J. Differential Equations, 2004(16), pp.1~11 (2004)

관련 논문AI추천

A weak solution for a class of the elliptic systems with even functional정택선, 최규흥장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호Existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic systemNguyen Viet Tuan대한수학회 · 대한수학회논문집2023 · 제38권 제3호Multiplicity of solutions of elliptic system using two critical point theorem남혜원강원경기수학회 · 한국수학논문집2017 · 제25권 제4호Nontrivial solutions for an elliptic system남혜원, 이성철강원경기수학회 · 한국수학논문집2015 · 제23권 제1호Multiplicity result of the solutions for a class of the elliptic systems with subcritical Sobolev exponents정택선, 최규흥강원경기수학회 · 한국수학논문집2015 · 제23권 제4호Weak solution for a class of the square growth nonlinear elliptic systems정택선, 최규흥장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제3호

이 간행물의 다른 논문 (20건)

Congruences on abundant semigroups with quasi-ideal S-adequate transversalsLili Wang, Aifa Wangpp. 1-8Crossed modules and strict Gr-categoriesNguyen Thu Thuy, Nguyen Tien Quang, Pham Thi Cucpp. 9-22Unramified scalar extensions of graded division algebras황윤성pp. 23-26ON f-DERIVATIONS FROM SEMILATTICES TO LATTICES연용호, 김경호pp. 27-36HERMITE-HADAMARD TYPE INEQUALITIES FOR GEOMETRIC-ARITHMETICALLY s-CONVEX FUNCTIONSFeng Qian, Ju Hua, Bo-Yan Xipp. 51-63
원문 보기