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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 note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −∆u = h(x)u in IR , where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence(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.
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)
In this paper we will investigate the existence of multiple solutions for the problem (P ) −∆pu+ g(x, u) = λ1h(x) |u|p−2 u, in Ω, u ∈ H 0 (Ω) where ∆pu = div ( |∇u|p−2 ∇u ) is the p-Laplacian operator, Ω ⊆ IR is a bounded domain with smooth boundary, h and g are bounded functions, N ≥ 1 and 1 < p < ∞. Using the Mountain Pass Theorem and the Ekeland(More)