We construct a family of singular solutions to some nonlinear partial differential equations which have resonances in the sense of a paper due to T.Kobayashi. The leading term of a solution in our family contains a logarithm, possibly multiplied by a monomial. As an application, we study nonlinear wave equations with quadratic nonlinearities. The proof is done by the reduction to a Fuchsian equation with singular coefficients.
"Logarithmic singularities of solutions to nonlinear partial differential equations." J. Math. Soc. Japan 60 (2) 603 - 630, April, 2008. https://doi.org/10.2969/jmsj/06020603