Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights

Using the potential theory, we establish the existence and the asypmtotic behavior of radial solutions for the following boundary value problem: {-1/A (A phi(|u'|)u')' = a(t)u(sigma) on (0, 1), A phi( |u'|)u'(0) = 0, u(1) = 0 , where sigma > 0, A is a positive differentiable function on (0, 1) and the nonnegative function phi is continuously differentiable on [0 , infinity ) such that for each t > 0, k(1) <=(t phi( t))'/phi( t) <= k(2) , where k(1) > 0 and k(2) > 0. The nonnegative nonlinearity a is required to satisfy some appropriate assumptions related to the Karamata regular variation theory. We end this paper by giving applications.