Existence and multiplicity of solutions for certain Dirichlet problems with nonlinearity depending on the derivative Original Research Article

We study existence and multiplicity of solutions for the problem u″(t)+u(t)+g(u′(t))=f(t), u(0)=u(π)=0, where f∈C[0,π] and View the MathML source has finite limits View the MathML source. The main tools used are the Lyapunov–Schmidt reduction principle and certain asymptotic methods.