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Information Center for Mathematical Science


Communications in Partial Differential Equations
( Vol. 23 NO.11 / (1998))
Global Bifurcation Results for Semilinear Elliptic Problems in $\mathbb R^N$
J. Giacomoni,
Pages. 1875-1927
Contents 1. Introduction
2. Auxiliary results
2.1 Rabinowitz theorem
3. First examle : Positive sublinear nonlinearities like $ f (u) = U^{\alpha} , \alpha =in ]0, 1[$
3.1 Main results
3.2 Existence and properties of solutions of $(P_R)$
3.3 Global bifurcation for problem (P)
4. Second example : sublinear nonlinearities like $f (u) = |u|^{p-1} u - |u|^{q-1} U, 1

4.1 Main result
4.2 A proiri bounds for the local problem
4.3 Existenceof a global branch of positive dolutions for the problem (P)
4.4 Generalization
5.Another example in the sublinear case
5.1 Main result
5.2 Local estimates for $(P_R)$
5.3 Existence of a global branch of solutions of (P)
6. An example in a superlinear case
6.1 Main result
6.2 A priori estimates for the solution of $(P_R)$
6.3 Global branch of solutions of (P)

Key words
Mathmatical Subject Classification