Semilinear elliptic problems with nonlinearities depending on the derivative
Arcoya, David ; del Toro, Naira
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003), p. 413-426 / Harvested from Czech Digital Mathematics Library
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We deal with the boundary value problem $$ \alignat2 -\Delta u(x) & = \lambda _{1}u(x)+g(\nabla u(x))+h(x), \quad && x\in \Omega \ u(x) & = 0, && x\in \partial \Omega \endalignat $$ where $\Omega \subset \Bbb R^N$ is an smooth bounded domain, $\lambda _{1}$ is the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions on $\Omega $, $h\in L^{\max \{2,N/2\}}(\Omega )$ and $g:\Bbb R^N\longrightarrow \Bbb R$ is bounded and continuous. Bifurcation theory is used as the right framework to show the existence of solution provided that $g$ satisfies certain conditions on the origin and at infinity.

Publié le : 2003-01-01
Classification:  35B32,  35B34,  35J25,  35J60,  35J65,  47J15 
@article{119398,
     author = {David Arcoya and Naira del Toro},
     title = {Semilinear elliptic problems with nonlinearities depending on the derivative},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {44},
     year = {2003},
     pages = {413-426},
     zbl = {1105.35038},
     mrnumber = {2025810},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119398}
}

Arcoya, David; del Toro, Naira. Semilinear elliptic problems with nonlinearities depending on the derivative. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 413-426. http://gdmltest.u-ga.fr/item/119398/

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