Some Surprising Results on a One-Dimensional Elliptic Boundary Value Blow-Up Problem

Y. J. Cheng

Abstract: In this paper we consider the one-dimensional elliptic boundary blow-up problem $$\left.\eqalign{ &\Delta_pu = f(u) \ \ (a < t < b) \cr &u(a)=u(b) = +\infty \cr} \right\} $$ where $\Delta_p u = \big(|u'(t)|^{p-2}u'(t)\big)'$ is the usual $p$-Laplace operator. We show that the structure of the solutions can be very rich even for a simple function $f$ which gives a leading that a simliar results might hold also in higher dimensional spaces

Keywords: boundary blow-up, multiplicity, concave and convex nonlinearity

Classification (MSC2000): 34B, 35J

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