Stuart, C. A.
Bifurcation without Frechet differentiability at the trivial solution
Mathematical Methods In The Applied Sciences
0170-4214
10.1002/mma.3409
38
16
3444-3463
20
Criteria for the bifurcation of small solutions of an equation F(lambda,u) = 0 from a line {(lambda,0): lambda is an element of R} of trivial solutions are usually based on properties of the DuF(lambda,0) at the trivial solutions, where the partial derivative is taken in the sense of Frechet. When this derivative only exists in some weaker sense, the situation charges considerably and much remains to be carried out to understand the conditions under which bifurcation takes place. This paper summarizes and extends one direction of research in this direction, where only Hadamard differentiability is required. In addition to presenting the abstract results, their application to the study of bound states of a class of nonlinear elliptic equations on R-N is also examined. Copyright (c) 2015 John Wiley & Sons, Ltd.
bifurcation;
nonlinear elliptic equation;
Wiley-Blackwell
Hoboken
2015