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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.
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 paper we study the existence of positive solutions for the problem −∆pu = u ∗−1 in Ω and u = 0 on ∂Ω where Ω is a perturbed annular domain (see definition in the introduction) and N > p ≥ 2. To prove our main results, we use the Concentration-Compactness Principle and variational techniques.
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)