Second-order Sturm–Liouville problems with asymmetric, superlinear nonlinearities Original Research Article

We consider the nonlinear Sturm–Liouville problem equation(1) View the MathML source equation(2) View the MathML source where p∈C1[0,π], q∈C0[0,π], with p(x)>0, x∈[0,π], and ci02+ci12>0, i=0,1. We suppose that View the MathML source is continuous and there exist increasing functions View the MathML source, and a constant B, such that View the MathML source and View the MathML source View the MathML source for all View the MathML source (thus the nonlinearity in (1) is superlinear as u(x)→∞, but linearly bounded as u(x)→−∞). We obtain solutions of (1)–(2) having specified nodal properties.