Electron. J. Diff. Eqns., Vol. 1996(1996), No. 01, pp 1--9.

On the number of solutions of boundary value problems involving the P-Laplacian

Hai Dang, Klaus Schmitt, & R. Shivaji

Abstract:
This paper is concerned with multiplicity questions for solutions of the boundary value problem
$(\varphi (u'))' + \lambda f(t, u)=0$ a less than t less than b
$$u(a)=u(b)=0. $$
where $\varphi$ is an odd, increasing homeomorphism on R, and $\lambda$ is a positive parameter. The tools employed are fixed point and continuation methods.

Submitted October 4, 1995. Published January 8, 1996.
Math Subject Classification: 34B15, 35J15, 35J85.
Key Words: p-Laplacian, radial solutions, boundary value problems.

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Hai Dang
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
e-mail: dang@math.msstate.edu
Klaus Schmitt
Department of Mathematics, University of Utah
Salt Lake City, UT 84112, USA
e-mail: schmitt@math.utah.edu
R. Shivaji
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
e-mail: shivaji@math.msstate.edu

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