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The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms
We consider, for and the homogeneous
Dirichlet problem for the equation in a
smooth bounded domain We prove that under
certain setting of the parameters and the problem admits
at least one positive solution. Using this result we prove that if
are arbitrarily fixed and is sufficiently small, then the
problem has a positive solution for all sufficiently large. In
addition, we show that converges uniformly to the distance function to
the boundary of as This convergence result is
new for nonlinearities involving a convection term.Comment: 18 page