Second order systems with nonlinear nonlocal boundary conditions

Positive solutions of a second-order nonlinear Robin problem involving the first-order derivative

“…For the cases of superlinear nonlinearity at ∞, the Bernstein-Nagumo type condition [7,9,25] is introduced to enable us to obtain the a priori estimate of the first-order derivative for associated boundary value problems. Our results generalize and extend the ones in [20,23], are strikingly different from the ones in [1-3, 8, 12, 14, 15, 17, 21] and also complement the main ones in [16,24].…”

Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence

“…Nonlinear functional BCs were investigated by Mawhin et al in [31], where the authors prove, by means of degree theory, the existence of a solution of a system of BVPs which, in the scalar case, reduces to…”

An affine Birkhoff--Kellogg type result in cones with applications to functional differential equations

“…allows to cover the interesting case of nonlinear and nonlocal boundary conditions (BCs) that can occur in the differential problems; there exists a wide literature on these kind of BCs, we refer the reader to the reviews [5,7,19,22,21,23,28] and the manuscripts [10,16,27]. We mention, in particular, the contributions of Mawhin and co-authors in this area of research, see for example [20]. Note that, in the applications, the functional B[•] can also take into account of the past state of the system.…”