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This paper deals with the generalized nonlinear third-order left focal problem at resonance $$\left\{\begin{array}{c}{\left(p\left(t\right)u^{\text{'}\text{'}}\left(t\right)\right)}^{\text{'}}-q\left(t\right)u\left(t\right)=f(t,u\left(t\right),u^{\text{'}}\left(t\right),u^{\text{'}\text{'}}\left(t\right)),t\in ]t_0,T[,m(u\left(t_0\right),u^{\text{'}\text{'}}\left(t_0\right))=0,n(u\left(T\right),u^{\text{'}}\left(T\right))=0,l(u\left(\xi \right),u^{\text{'}}\left(\xi \right),u^{\text{'}\text{'}}\left(\xi \right))=0,\hfill \end{array}\right.$$ where the nonlinear term is a Carathéodory function and contains explicitly the first and second-order derivatives of the unknown function. The boundary conditions that we study are quite general, involve a linearity and include, as particular cases, Sturm-Liouville boundary conditions. Under certain growth conditions on the nonlinearity, we establish the existence of the nontrivial solutions by using the...