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Multiplicity of solutions for a nonlinear boundary value problem in the upper half-space

Marcelo Furtado (UnB)

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We obtain multiple solutions for the nonlinear boundary value problem \(-\Delta u-\dfrac{1}{2}\left( x\cdot abla u\right) = f(\lambda,x,u), \mbox{ in }\mathbb{R}_{+}^{N}, \qquad \dfrac{\partial u}{\partial u}=g(\mu,x',u), \mbox{ on } \partial \mathbb{R}_{+}^{N},\) where $\mathbb{R}^N_+ = {(x’,x_N) : x’ \in \mathbb{R}^{N-1},\,x_N>0 }$ is the upper half-space and $\lambda,\,\mu>0$ are parameters. We consider sublinear, linear and superlinear cases and the function $g$ has critical growth.

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