Existence and multiplicity of solutions for anisotropic elliptic equation
Abstract
In this article we study the nonlinear problem
$$\left\{ \begin{array}{lr}
-\sum_{i=1}^{N}\partial_{x_{i}}a_{i}(x,\partial_{x_{i}}u)+ b(x)~|u|^{P_{+}^{+}-2}u =\lambda f(x,u) \quad in \quad \Omega\\
u=0 \qquad on \qquad \partial\Omega
\end{array} \right.$$
Using the variational method, under appropriate assumptions on $f$, we obtain a result on existence and multiplicity of solutions.
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References
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