H. Q. Toan

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In this paper, we obtain some new results on the existence of non-negative solutions for systems of the form (−∆ + qi)ui = μimiui + n ∑ j=1;j 6=i aijuj + fi(x, u1, ..., un) in R , i = 1, ..., n, where each of the qi are positive potentials satisfying lim|x|→+∞ qi(x) = +∞, each of the mi are bounded positive weights, each of the aij, i 6= j, are bounded(More)
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)|∇u|p−2∇u) + b(x)|u|p−2u = f(x, u), p ≥ 2 in an unbounded domain Ω ⊂ RN , N ≥ 3, with sufficiently smooth bounded boundary ∂Ω, where h(x) ∈ Lloc(Ω), Ω = Ω ∪ ∂Ω, h(x) ≥ 1 for all x ∈ Ω. The proof of main results(More)
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