Positive solutions for a Minkowski-curvature equation with indefinite weight and super-exponential nonlinearity

We investigate the existence of positive solutions for a class of Minkowski-curvature equations with indefinite weight and nonlinear term having superlinear growth at zero and super-exponential growth at. infinity. As an example, for the equation(u'/root 1+(u')(2)) + a(t)(e(up) - 1) = 0,where p > 1 and a(t) is a sign-changing function satisfying the mean-value condition integral(T)(0) a(t)dt < 0, we prove the existence of a positive solution for both periodic and Neumann boundary conditions. The proof relies on a topological degree technique.