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Si considera il problema al contorno $-\Delta u=f(x,u)+\epsilon\psi(x,u)$ in $\Omega$ , $u|\partial\Omega=0$ , dove $\Omega\in\mathbb{R}^{n}$ è un aperto limitato e connesso ed $\epsilon$ è un parametro reale. Si prova che, se $f(x,s)+\epsilon\psi(x,s)$ è «superlineare» ed $\epsilon$ è abbastanza piccolo, il problema precedente ha almeno tre soluzioni distinte.

Un théorème de valeurs intermédiaires dans les espaces de Sobolev et applications

Amina Chabi, Alain Haraux (1985)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Une méthode numérique pour le calcul des points de retournement. Application à un problème aux limites non-linéaire. I. Etude théorique et expérimentation de la méthode.

J.C. Paumier (1981)

Numerische Mathematik

Unfolding Bifucations of an Elliptic Boundary Value Problem.

H-O. Peitgen, A.J. Tromba (1984)

Mathematische Zeitschrift

Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types.

Boglaev, Igor (2005)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Uniqueness and regularity properties of linear operators and their applications

T. B. Boev (1987)

Banach Center Publications

Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions.

Zhang, Kewei (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Uniqueness for positive solutions of $p$ -Laplacian problem in an annulus

Eric Nabana (1999)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Uniqueness of global positive solution branches of nonlinear elliptic problems.

Marco Holzmann, Hansjörg Kielhöfer (1994)

Mathematische Annalen

Uniqueness of least energy solutions to a semilinear elliptic equation in R2.

Chang-Shou Lin (1994)

Manuscripta mathematica

Uniqueness of solutions for some elliptic equations with a quadratic gradient term

David Arcoya, Sergio Segura de León (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study a comparison principle and uniqueness of positive solutions for the homogeneous Dirichlet boundary value problem associated to quasi-linear elliptic equations with lower order terms. A model example is given by $- Δ u + λ \frac{{| \nabla u |}^{2}}{u^{r}} = f (x), λ, r > 0 .$ The main feature of these equations consists in having a quadratic gradient term in which singularities are allowed. The arguments employed here also work to deal with equations having lack of ellipticity or some dependence on u in the right hand side. Furthermore, they...

Uniqueness of the Solution of a Semilinear Boundary Value Problem.

S.B. Angenet (1985)

Mathematische Annalen

Uniqueness of weak solution for nonlinear elliptic equations in divergence form.

Zhang, Xu (2000)

International Journal of Mathematics and Mathematical Sciences

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