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).
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.
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 5 in Ω,u(x) > 0 in Ω and u = 0 on ∂ Ω, where Ω ⊂ R N , 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 on(More)
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