Semilinear elliptic equations with sublinear indefinite nonlinearities

Abstract

We prove existence, multiplicity and bifurcation results for a family of semilinear Neumann problems with nonlinear terms that are indefinite in sign and exhibit sublinear growth near zero. The solutions are non-negative, but the combined effect of indefiniteness and the non-Lipschitz character of the nonlinear term yields solutions which may vanish on large sets. Combining variational methods with bifurcation analysis and the sub- and super-solution