IJPAM: Volume 53, No. 3 (2009)

EXACT MULTIPLICITY OF SOLUTIONS FOR
$P$-LAPLACE TYPE DIFFERENTIAL EQUATIONS

Yuanji Cheng
Institute of Technology
Malmö University
Malmö, SE-205 06, SWEDEN
e-mail: yuanji.cheng@mah.se


Abstract.In this paper we study multiple solutions for boundary value problem of $p$-Laplace type equation

\begin{displaymath}\left\{ \begin{array}{lll} - (\varphi( u')) ' = \lambda \psi... ... \\ \quad u(-T)=0, \quad u(T)=0. \\ \end{array} \right. \end{displaymath}

There are lots of works devoted to such boundary value problem with odd function $ \varphi $ and almost no known result for the equation with non-odd function $\varphi.$ In this paper we study a particular non-odd case, e.g. $\varphi( s)= \alpha s^{p-1}, s \ge 0, \varphi( s)= -\beta \vert s\vert^{q-1}, s \le 0.$ We prove several exact multiplicity results for the solutions to the above equation.

Received: May 10, 2009

AMS Subject Classification: 34B15, 35J65, 49K20

Key Words and Phrases: nonlinear boundary value problem, nonlinear boundary value problems for linear elliptic PDE, boundary value problem for nonlinear elliptic PDE

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 3