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).
This article concerns with the problem ?div(jruj m?2 ru) = hu q + u m ?1 ; in R N : Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of > 0 such that there are at least two non-negative solutions for each in (0;).
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 study the existence of positive solutions for the problem −∆pu = u p * −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.