Search

In this paper, we study the existence and multiplicity solutions for the following Klein-Gordon-Maxwell system ∫-Δu + V(x)u - (2ω + ϕ)ϕu = f (x, u), x ∈ R³, Δϕ = (ω + ϕ)u², x ∊ R³, where ω > 0 is a constant and the nonlinearity f (x, u) is either asymptotically linear in u at infinity or the primitive of f (x, u) is of 4-superlinear growth in u at infinity. Under some suitable assumptions, the existence and multiplicity of solutions are proved by using the Mountain Pass theorem and the fountain theorem, respectively. [ABSTRACT FROM AUTHOR]

In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter λ > 0 varies. In our first result, the superlinear perturbation has an arbitrary growth and we obtain the existence of a solution for the problem by using the sub-supersolution method. For the second result, the superlinear perturbation has subcritical growth and we employ the Mountain Pass Theorem to show the existence of a second solution. [ABSTRACT FROM AUTHOR]

In this paper we show the existence and multiplicity of positive solutions using the sub-supersolution method and Mountain Pass Theorem in a general singular system which the operator is not homogeneous neither linear. [ABSTRACT FROM AUTHOR]

We study the following class of double-phase nonlinear eigenvalue problems − div [φ(x, ∣∇u∣)∇u + ψ(x, ∣∇u∣)∇u] = λ f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain from RN with smooth boundary and the potential functions φ and ψ have (p1(x); p2(x)) variable growth. The main results of this paper are to prove the existence of a continuous spectrum consisting in a bounded interval in the near proximity of the origin, the fact that the multiplicity of every eigenvalue located in this interval is at least two and to establish the existence of infinitely many solutions for our problem. The proofs rely on variational arguments based on the Ekeland's variational principle, the mountain pass theorem, the fountain theorem and energy estimates. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of quasilinear elliptic equations with Φ-Laplacian operator and critical growth. Using the symmetric mountain pass theorem and the concentration-compactness principle, we demonstrate that there exists λi>0 such that our problem admits i pairs of nontrivial weak solutions provided λ∈(0,λi). [ABSTRACT FROM AUTHOR]