## A study of eigenvalue and bifurcation problems for nonlinear elliptic partial differential equations via topological continuation methodsUniversité Catholique de Louvain, Institut de mathématique pure et appliquée, 1982 - Mathematics - 173 pages |

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_(id arguments similar Assume there exists bifurcation diagram bifurcation theorem boundary conditions boundary value problem bounded characteristic value compact completely continuous consider contradiction convergent subsequence COROLLARY deduce defined definition of f degLS(id denote dLS(id e.g. Figure eigenvalue established exists a continuum exists a sequence exists a solution f satisfy following lemma given implicit function theorem implies let f LF(u linear Lipschitz continuous maximum principle negative solution neighbourhood nonlinearity f norm numerical obtain the following ordinary differential equations partial differential equations perturbation phase plane phase portrait positive solutions precompact Proof secondary bifurcations sequence of solutions solution branches solution of 10.1 solution of 3.10 solution of 9.9 solution structure solutions of type solutions X.u spurious solutions subsequence converging theorem 3.1 trivial solution x e n X L F(u Xf(u XF(v zero Zorn's lemma