An application of a variational theorem of mixed type to a superlinear elliptic problem

We prove the existence of four solutions for the superlinear subcritical elliptic problem - Delta u = lambda u - (u(-))(p) - te(1) in Omega, u = 0 on partial derivative Omega, when t > 0, lambda(j) < lambda < lambda(j+1) and lambda is close enough to lambda(j+1) for j greater than or equal to 1 (here e(1) is the positive eigenfunction corresponding to lambda(1) and (lambda(i))(i greater than or equal to 1) is the sequence of the eigenvalues of -Delta in H-0(1)(Omega)). (C) 1999 Academic Press.