A History of Researches of Jumping Problems in Elliptic Equations

  • Park, Q-Heung (Department of Mathematics, Inha University) ;
  • Tacksun Jung (Department of Mathematics, Kunsan National University)
  • Published : 2002.12.01


We investigate a history of reseahches of a nonlinear elliptic equation with jumping nonlinearity, under Dirichlet boundary condition. The investigation will be focussed on the researches by topological methods. We also add recent researches, relations between multiplicity of solutions and source terms of tile equation when the nonlinearity crosses two eigenvalues and the source term is generated by three eigenfunctions.



  1. Proc. Roy. Soc. Edin. v.84 A Multiplicity result for a class of elliptic boundary value problems Amann, H.;Hess, P.
  2. Cambridge Studies in Advanced Math. no.34 A primer of nonlinear analysis Ambrosetti, A.;Prodi, G.;
  3. Studia Math v.20 The multiplicity of solutions and geometry of the nonlinear elliptic equation Choi, Q.H.;Chun, S.;Jung, T.
  4. J. Math. Pures et Appl. v.57 On the ranges of certain weakly nonlinear elliptic partial differential equations Dancer, E.N.
  5. J. Math. Anal. Appl. v.86 On the number of solutions of a nonlinar Dirichlet problem Lazer, A.C.;McKenna, P.J.
  6. J. Math. Anal. Appl. v.107 Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems Lazer, A.C.;McKenna, P.J.
  7. Comm.in P.D.E. v.11 Critical points theory and boundary value problems the nonlinearities crossing multiple eigenvalues II Lazer, A.C.;McKenna, P.J.
  8. Lecture Note Series No.11, Research Institude of Math. Topolgical methods for asymmetric boundary value problem McKenna, P.J.
  9. Rocky Mountain Math. J. v.16 Boundary value problems with jumping nonlinearities Schmitt, K.