000216649 001__ 216649 000216649 005__ 20181203024155.0 000216649 0247_ $$2doi$$a10.1002/mma.3409 000216649 022__ $$a0170-4214 000216649 02470 $$2ISI$$a000364646400007 000216649 037__ $$aARTICLE 000216649 245__ $$aBifurcation without Frechet differentiability at the trivial solution 000216649 260__ $$bWiley-Blackwell$$c2015$$aHoboken 000216649 269__ $$a2015 000216649 300__ $$a20 000216649 336__ $$aJournal Articles 000216649 520__ $$aCriteria 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. 000216649 6531_ $$abifurcation 000216649 6531_ $$anonlinear elliptic equation 000216649 700__ $$aStuart, C. A. 000216649 773__ $$j38$$tMathematical Methods In The Applied Sciences$$k16$$q3444-3463 000216649 909C0 $$0252057$$pANA 000216649 909CO $$particle$$ooai:infoscience.tind.io:216649 000216649 937__ $$aEPFL-ARTICLE-216649 000216649 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL 000216649 980__ $$aARTICLE