RT Journal Article
T1 Existence and multiplicity results for some generalized Hammerstein equations with a parameter
A1 López Somoza, Lucía
A1 Minhós, Feliz
K1 Hammerstein equations
K1 Nonlinear boundary value problems
K1 Parameter dependence
K1 Degree theory
K1 Fixed points in cones
AB This paper considers the existence and multiplicity of fixed points for the integral operatorTu(t)=λ∫T0k(t,s)f(s,u(s),u′(s),…,u(m)(s))ds,t∈[0,T]≡I,where λ>0 is a positive parameter, k:I×I→R is a kernel function such that k∈Wm,1(I×I), m is a positive integer with m≥1, and f:I×Rm+1→[0,+∞[ is an L1-Carathéodory function.The existence of solutions for these Hammerstein equations is obtained by fixed point index theory on new type of cones. Therefore some assumptions must hold only for, at least, one of the derivatives of the kernel or, even, for the kernel on a subset of the domain. Assuming some asymptotic conditions on the nonlinearity f, we get sufficient conditions for multiplicity of solutions.Two examples will illustrate the potentialities of the main results, namely the fact that the kernel function and/or some derivatives may only be positive on some subintervals, which can degenerate to a point. Moreover, an application of our method to general Lidstone problems improves the existent results in the literature in this field
PB Springer
YR 2019
FD 2019
LK http://hdl.handle.net/10347/21100
UL http://hdl.handle.net/10347/21100
LA eng
NO López-Somoza, L., Minhós, F. Existence and multiplicity results for some generalized Hammerstein equations with a parameter. Adv Differ Equ 2019, 423 (2019). https://doi.org/10.1186/s13662-019-2359-y
NO First author was partially supported by Xunta de Galicia (Spain), project EM2014/032, AIE Spain and FEDER, grants MTM2013-43014-P, MTM2016-75140-P, and FPU scholarship, Ministerio de Educación, Cultura y Deporte, Spain. F. Minhós was supported by FCT-Fundação para a Ciência e a Tecnologia, via project UID/MAT/ 04674/2019
DS Minerva
RD 26 abr 2026