Solvability of a nonlinear two-point boundary value problem at resonance II Original Research Article

In this article we apply the Leray–Schauder continuation method to obtain existence theorems of solutions for (i) u″+u+g(x,u)=h in (0,π), u(0)=u(π)=0 in which the nonlinearity g grow superlinearly in u in one of directions u→∞ and u→−∞, and may grow sublinearly in the other, and for (ii) −u″−u+g(x,u)=h in (0,π), u(0)=u(π)=0 in which the nonlinearity g has no growth restriction in u as |u|→∞. The L1(0,π) function h may satisfy View the MathML source, where α,β⩾0, View the MathML source, and View the MathML source.