On equivalent conditions for the solvability of the equation \((p(t)x')'+f(t,x)=h(t)\) satisfying linear boundary conditions with \(f\) restricted by linear growth conditions
The author examines the existence of solutions to nonlinear second-order boundary value problems with linear boundary conditions on finite intervals. The concept of generalized resonant point is introduced to generalize the term resonance point (natural frequency or eigenvalue) for the case of linear analogues. The nonlinearity in the differential equation is assumed to be of the form of a Carathéodory function. The solvability of the problem is investigated, and an existence theorem is proved. For some particular cases of the problem, sufficient conditions for the existence of solutions are provided.
scientific article; zbMATH DE number 1449172
scientific article