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In this paper we study the following problem: −Δ p u + |u| p−2 u = k(x) f (u) + h(x) , x ∈ R N , where u ∈ W 1,p (R N) , u > 0 in R N. Under appropriate assumptions on k , h and f , we prove that problem has at least two positive solutions.
In this paper, we are concerned with the third-order quasilinear ordinary differential equation (Φ p (u)) = f (t, u, u , u), 0 < t < 1, with the nonlinear boundary conditions u(0) = 0, g(u (0), u (0)) = A, h(u (1), u (1)) = B or u(0) = C, L(u (0), u (1)) = 0, R(u (0), u (1), u (0), u (1)) = 0, 4 → R are continuous, which occurs in the study of the p-Laplace… (More)