Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation

Existence of solutions for a nonlinear fourth order ordinary differential equation arising in beam theory is considered. We obtain solutions by a degree argument under a non-asymptotic condition on the nonlinear terms of the problem. Moreover, assuming a potential Landesman-Lazer condition, we prove the existence of at least one solution by variational methods.Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin