# ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING p-LAPLACIAN IN AN UNBOUNDED DOMAIN

• Published : 2011.11.30

#### Abstract

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

#### Acknowledgement

Supported by : NAFOSTED

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#### Cited by

1. ON A NEUMANN PROBLEM AT RESONANCE FOR NONUNIFORMLY SEMILINEAR ELLIPTIC SYSTEMS IN AN UNBOUNDED DOMAIN WITH NONLINEAR BOUNDARY CONDITION vol.51, pp.6, 2014, https://doi.org/10.4134/BKMS.2014.51.6.1669