Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 83, pp. 1-14.

Title: Remarks on least energy solutions for
       quasilinear elliptic problems in $R^N$

Authors: Joao Marcos do O (Univ. Fed. Paraiba, Brazil)
  Everaldo S. Medeiros (Univ. Fed. Paraiba, Brazil)

Abstract: 
  In this work we establish some properties of the solutions
  to the quasilinear second-order problem
  $$
   -\Delta_p w=g(w)\quad \hbox{in }  \mathbb{R}^N
  $$
  where $\Delta_p u=\mathop{\rm div}(|\nabla u|^{p-2}\nabla u)$
  is the $p$-Laplacian  operator and $ 1<p\leq N $. We study a
  mountain pass characterization of least energy solutions of this
  problem. Without assuming the monotonicity of the function
  $t^{1-p}g(t)$, we show that the Mountain-Pass value gives the
  least energy level. We also prove the exponential decay of the
  derivatives of the solutions.
 
Submitted June 3, 2003. Published August 11, 2003.
Math Subject Classifications: 35J20, 35J60.
Key Words: Variational methods; minimax methods;
           superlinear elliptic problems; p-Laplacian;
           ground-states; moutain-pass solutions