DOI QR코드

DOI QR Code

EXISTENCE OF THE SOLUTIONS FOR THE SINGULAR POTENTIAL ELLIPTIC SYSTEM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • 투고 : 2012.01.19
  • 심사 : 2012.03.15
  • 발행 : 2012.03.30

초록

We investigate the multiple solutions for a class of the elliptic system with the singular potential nonlinearity. We obtain a theorem which shows the existence of the solution for a class of the elliptic system with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and critical point theory.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

참고문헌

  1. A. Castro and J. Cossio, Multiple Solutions for a nonlinear Dirichlet problem, SIAM J. Math. Anal. 25, (6) (1994), 1554-1561. https://doi.org/10.1137/S0036141092230106
  2. A. Castro and A. C. Lazer, Critical point theory and the number of solutions of a nonlinear Dirichlet problem, Ann. Mat. Pura Appl. 120 (4) (1979), 113-137. https://doi.org/10.1007/BF02411940
  3. M. Degiovanni, Homotopical properties of a class of nonsmooth functions, Ann. Mat. Pura Appl. 156 (1990), 37-71. https://doi.org/10.1007/BF01766973
  4. A. Groli, A. Marino and C. Saccon, Variational theorems of mixed type and asymptotically linear variational inequalities, Topol. Methods Nonlinear Anal. 12 (1998), 109-136. https://doi.org/10.12775/TMNA.1998.031
  5. K.S. Ha and Y.H. Lee, Existence of multiple positive solutions of singular boundary value problems, Nonlinear Anal. TMA, 28 (1997), 1429-1438. https://doi.org/10.1016/0362-546X(95)00231-J
  6. K. Lan and R.L. Webb, Positive solutions of semilinear equation with singularities, J. Differential Equations, 148 (1998), 407-421. https://doi.org/10.1006/jdeq.1998.3475
  7. A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal. TMA, 31 (7) (1998), 895-908. https://doi.org/10.1016/S0362-546X(97)00446-X
  8. P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. in Math. 6, Amer. Math. Soc., Providence, RI, 1986.