Abstract
Localized radial solutions for a nonlinear p-Laplacian equation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:math>
Highlights
In this paper we look for solutions u : RN → R of the nonlinear partial differential equation
By Lemma 3.5, if d > d0 and d close to d0 u(r, d) has at most one zero
Summary
In this paper we look for solutions u : RN → R of the nonlinear partial differential equation (1.1). McLeod, Troy and Weissler studied the radial solutions of the above mentioned equation in [5]. In this paper they made a remark that their result could be extended to the p-Laplacian. Serrin and Tang [9] have proved existence of radial solutions to a p-Laplacian equation with Dirichlet and Neumann boundary conditions. We assume that u(x) = u(|x|) and let r = |x| In this case (1.1)-(1.2) becomes the nonlinear ordinary differential equation (1.3). We first solve the initial value problem r rN−1|u |p−2u = − sN−1f (u(s))ds u(0) = d ≥ 0.
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