doi:10.1017/S0308210513000486
ISI:000343761000008
Stuart, C. A.
Bifurcation at isolated singular points of the Hadamard derivative
Cambridge, Royal Society of Edinburgh Scotland Foundation, Cambridge
http://infoscience.epfl.ch/record/204182/files/S0308210513000486.pdf
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.
2014-12-30T08:44:20Z
http://infoscience.epfl.ch/record/204182
http://infoscience.epfl.ch/record/204182
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