Some Remarks on a Class of Nonuniformly Elliptic Equations of p-Laplacian Type
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Abstract
This paper deals with the existence of weak solutions in W 0 1 (Ω) to a class of elliptic problems of the form in a bounded domain Ω of ℝ N . Here a satisfies for all ξ∈ℝ N , a.e. x∈Ω,
\(h_{0}\in L^{\frac{p}{{p-1}}}(\Omega)\)
, h 1∈L loc 1 (Ω), h 1(x)≧1 for a.e. x in Ω; λ 1 is the first eigenvalue for −Δ p on Ω with zero Dirichlet boundary condition and g, h satisfy some suitable conditions.
$$-\mathop{\mathrm{div}}({a({x,\nabla u})})=\lambda_{1}\left|u\right |^{p-2}u+g\left(u\right)-h$$
$$\left|{a\left({x,\xi}\right)}\right|\leqq c_{0}\left({h_{0}\left(x\right)+h_{1}\left(x\right)\left|\xi\right|^{p-1}}\right)$$
Keywords
p-Laplacian Nonuniform Landesman-Laser Elliptic Divergence form Landesman-Laser typeMathematics Subject Classification (2000)
35J20 35J60 58E05Preview
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