A cantilever equation with nonlinear boundary conditions

Solutions of perturbed Hammerstein integral equations with applications

“…according to the displacement registered in the right end. Various methods were used to deal with the existence of solutions of the boundary value problem (BVP) (1.1)-(1.2), for example variational methods in [9,78], iterative methods in [1,62,64] and topological methods in [36].…”

Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains

“…This type of problem has been tackled in the past in the case of second and higher order BVPs in [7,24,25,42,52,53,57]. Since in [0, 1] × [0, 1] the kernel k 1 is non-positive only for…”

Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions

“…In the case of the systems –, the BCs can be interpreted as a cable‐beam model with two devices of feedback control, where the displacement of the left end of the cable is related to displacement of another point ξ of the cable and the bending moment in the right end of the beam depends upon the displacement registered in a point η of the string. We point out that not necessarily the response of the controllers needs to be of linear type; for example, this happens with conditions of the type we refer to for more details regarding the illustration of nonlinear controllers on a beam.…”

“…we refer to [24] for more details regarding the illustration of nonlinear controllers on a beam. Our approach allows us to deal with a larger class of nonlinear, nonlocal BCs, with one example given by the BCs…”

“…where H ij , L ij are continuous functions. For earlier contributions on problems with nonlinear BCs, we refer the reader to [24][25][26][27][28][29][30][31][32][33] and references therein.…”