Electron. J. Diff. Eqns., Vol. 2001(2001), No. 66, pp. 1-6.

Existence of solutions to a superlinear p-Laplacian equation

Shibo Liu

Using Morse theory, we establish the existence of solutions to the equation
$-\Delta_p u = f(x,u)$
with Dirichlet boundary conditions. We assume that $\int_0^s f(x,t)\,dt$ lies between the first two eigenvalues of the p-Laplacian.

Submitted August 21, 2001. Published October 11, 2001.
Math Subject Classifications: 49J35, 35J65, 35B34.
Key Words: p-Laplacian, critical group.

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Shibo Liu
Institute of Mathematics
Academy of Mathematics and Systems Sciences
Academia Sinica
Beijing, 100080, P. R. China
e-mail: liusb@math08.math.ac.cn

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