Claudianor Oliveira Alves

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we are concerned with perturbations of the Hamiltonian system of the type c L(t)q + W&, q) = 0, t E R, WI where q = (ql, , qN) E WN, W E C1(W x WN,R), and L(t) E C(W,WN2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS). @ 2003 Elsevier Science Ltd. All rights reserved.(More)
This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff type − [ M (∫ Ω |∇u|2 dx )] Δu = λ f (x,u)+u in Ω,u(x) > 0 in Ω and u = 0 on ∂Ω, where Ω ⊂ RN , for N=1,2 and 3, is a bounded smooth domain, M and f are continuous functions and λ is a positive parameter. Our approach is based(More)
In this article, we use the Galerkin method to show the existence of solutions for the following elliptic equation with convection term −∆u = h(x, u) + λg(x,∇u) u(x) > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain, λ ≥ 0 is a parameter, h has sublinear and singular terms, and g is a continuous function.
We give a method for obtaining radially symmetric solutions for the critical exponent problem ?u + a(x)u = u q + u 2 ?1 in R N u > 0 and R R N jruj 2 < 1 where, outside a ball centered at the origin, the non-negative function a is bounded from below by a positive constant ao > 0. We remark that, diierently from the literature, we do not require any(More)
This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the form −∆u + a(x)u = h(x)u−γ in R where a, h are given, not necessarily continuous functions, and γ is a positive number. We explore both situations where a, h are radial functions, with a being eventually identically zero, and(More)
We prove that the semilinear elliptic equation −Δu f u , inΩ, u 0, on ∂Ω has a positive solution when the nonlinearity f belongs to a class which satisfies μt ≤ f t ≤ Ct at infinity and behaves like t near the origin, where 1 < q < N 2 / N − 2 if N ≥ 3 and 1 < q < ∞ if N 1, 2. In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the(More)