• Title/Summary/Keyword: generalized mountain pass geometry

Search Result 2, Processing Time 0.019 seconds

NONLINEAR BIHARMONIC EQUATION WITH POLYNOMIAL GROWTH NONLINEAR TERM

  • JUNG, TACKSUN;CHOI, Q-HEUNG
    • Korean Journal of Mathematics
    • /
    • v.23 no.3
    • /
    • pp.379-391
    • /
    • 2015
  • We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

NONLINEAR BIHARMONIC PROBLEM WITH VARIABLE COEFFICIENT EXPONENTIAL GROWTH TERM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
    • /
    • v.18 no.3
    • /
    • pp.277-288
    • /
    • 2010
  • We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.