Bifurcation at isolated singular points of the Hadamard derivative

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.


Published in:
Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics, 144, 5, 1027-1065
Year:
2014
Publisher:
Cambridge, Cambridge Univ Press
ISSN:
0308-2105
Laboratories:




 Record created 2014-12-30, last modified 2018-09-13


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