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Let $G : ℂ^{n} \times ℂ^{r} \to ℂ$ be a holomorphic family of functions. If $Λ \subset ℂ^{n} \times ℂ^{r}$ , $π_{r} : ℂ^{n} \times ℂ^{r} \to ℂ^{r}$ is an analytic variety then $Q_{Λ} (G) = (x, u) \in ℂ^{n} \times ℂ^{r} : G (\cdot, u) h a s a c r i t i c a l p o i n t i n Λ \cap π_{r}^{- 1} (u)$ is a natural generalization of the bifurcation variety of G. We investigate the local structure of $Q_{Λ} (G)$ for locally trivial deformations of $Λ ₀ = π_{r}^{- 1} (0)$ . In particular, we construct an algorithm for determining logarithmic stratifications provided G is versal.

New solutions of equations on $ℝ^{n}$

Edward Norman Dancer (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Nonlinear Variational Inequalities Depending on a Parameter

Goeleven, D., Théra, M. (1995)

Serdica Mathematical Journal

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.

Notes on some recent methods in bifurcation theory

D. R. J. Chillingworth (1985)

Banach Center Publications

On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential

Manuela Chaves, Jesús García-Azorero (2006)

Journal of the European Mathematical Society

We present some results concerning the problem $- Δ u = λ \frac{u}{{| x |}^{2}} + u^{q}$ , $u > 0$ in $Ω$ , ${u |}_{\partial Ω} = 0$ , where $0 < q < (N + 2) / (N - 2)$ , $q \neq 1$ , $λ \geq 0$ and $Ω$ is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.

On infinitely many solutions of a semilinear elliptic eigenvalue problem

Jörn Lembcke (1989)

Commentationes Mathematicae Universitatis Carolinae

On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.

L. Reinhart (1982)

Numerische Mathematik

On the numerical solution of perturbed bifurcation problems.

Elgindi, M.B.M., Langer, R.W. (1995)

International Journal of Mathematics and Mathematical Sciences

On two problems studied by A. Ambrosetti

David Arcoya, José Carmona (2006)

Journal of the European Mathematical Society

We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected $C$ ( $\supset$ -shape). Next, we show that there is a relationship between these two problems.

Remarks on inflated mappings

Vladimír Janovský, Drahoslava Janovská (1987)

Commentationes Mathematicae Universitatis Carolinae

Remarks on Krasnoselskii bifurcation theorem

Raffaele Chiappinelli (1989)

Commentationes Mathematicae Universitatis Carolinae

Résolution des équations semilinéaires avec la partie linéaire à noyau de dimension infinie via des applications A-propres [Book]

Wiesław Krawcewicz (1990)

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