Stuart, C. A.
Bifurcation at isolated singular points of the Hadamard derivative
Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics
0308-2105
10.1017/S0308210513000486
144
5
1027-1065
39
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.
Royal Society of Edinburgh Scotland Foundation, Cambridge
Cambridge
2014
http://infoscience.epfl.ch/record/204182/files/S0308210513000486.pdf;