The aim of this paper is to prove some existence and multiplicity results for functionals of type \[ J(u) = \int_\Omega A(x,u)|\nabla u|^2 dx - \int_\Omega G(x,u) dx,\qquad u \in {\cal D}\subset H^1_0(\Omega),\] with bounded domain $\Omega$ in $\R^N$. Since, in general, $J$ is not G\^ateaux differentiable in ${\cal D}$, we study its restriction on the Banach space $X = H^1_0(\Omega) \cap L^\infty(\Omega)$ and apply some abstract existence and multiplicity theorems involving a variant of condition $(C)$ below.
Multiple solutions of some nonlinear variational problems
CANDELA, Anna Maria;
2006-01-01
Abstract
The aim of this paper is to prove some existence and multiplicity results for functionals of type \[ J(u) = \int_\Omega A(x,u)|\nabla u|^2 dx - \int_\Omega G(x,u) dx,\qquad u \in {\cal D}\subset H^1_0(\Omega),\] with bounded domain $\Omega$ in $\R^N$. Since, in general, $J$ is not G\^ateaux differentiable in ${\cal D}$, we study its restriction on the Banach space $X = H^1_0(\Omega) \cap L^\infty(\Omega)$ and apply some abstract existence and multiplicity theorems involving a variant of condition $(C)$ below.File in questo prodotto:
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