TY - EJOUR
DO - 10.1017/S0308210513000486
AB - For Banach spaces X and Y, we consider bifurcation from the line of trivial solutions for the equation F(lambda, u) = 0, where F : R x X -> Y with F(lambda, 0) = 0 for all lambda is an element of R. The focus is on the situation where F(lambda, center dot) is only Hadamard differentiable at 0 and Lipschitz continuous on some open neighbourhood of 0, without requiring any Frechet differentiability. Applications of the results obtained here to some problems involving nonlinear elliptic equations on R-N, where Frechet differentiability is not available, are presented in some related papers, which shed light on the relevance of our hypotheses.
T1 - Bifurcation at isolated singular points of the Hadamard derivative
IS - 5
DA - 2014
AU - Stuart, C. A.
JF - Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics
SP - 1027-1065
VL - 144
EP - 1027-1065
PB - Royal Society of Edinburgh Scotland Foundation, Cambridge
PP - Cambridge
N1 - National Licences
ID - 204182
SN - 0308-2105
UR - http://infoscience.epfl.ch/record/204182/files/S0308210513000486.pdf
ER -