and Applied Analysis 3 Definition 2.2. Let f be any real-valued function and ν ∈ 0, 1 . The left discrete fractional difference and the right discrete fractional difference operators are, respectively, defined as tΔaf t ΔtΔ − 1−ν a f t 1 Γ 1 − ν Δ t ν−1 ∑ s a t − s − 1 −ν f s , t ≡ a − ν 1 mod1 , bΔt f t −ΔbΔ 1−ν t f t 1 Γ 1 − ν −Δ b ∑ s t 1−ν s − t − 1 −ν f s , t ≡ b ν − 1 mod1 . 2.2 Definitio...

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

Abstract We establish the existence of at least two solutions Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and singular term. The associated energy functional is nondifferentiable, hence usual variational techniques do not work. shall use novel approach in tackling sequence $C^{1}$ C ...

This paper is concerned with a kind of non-Newtonian filtration equation nonlinear sources and singularities. Based on the mountain pass theorem variational methods, sufficient criterion for new results periodic wave solutions has been provided. Here not only structure more general practical than existing works but conditions imposed are concise. Consequently, compared previous singular equatio...

In this paper we consider a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP) with a P 0 function. PPA was originally proposed by Martinet and further developed by Rockafel-lar for monotone variational inequalities and monotone operator problems. PPA is known to have nice convergence properties under mild conditions. However, until now, it has been applied m...

In this paper we consider a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP) with a P 0 function. PPA was originally proposed by Martinet and further developed by Rockafellar for monotone variational inequalities and monotone operator problems. PPA is known to have nice convergence properties under mild conditions. However, until now, it has been applied ma...

LRES, Faculty of Sciences Tunis, University Tunis El Manar, Tunisia EM [email protected] KW Asymptotically linear % variational method Schr?dinger equations Cerami sequence KR nema In this paper, we investigate a quasilinear problem under Dirichlet boundary condition in regular domain with asymptotically nonlinearities. We use version the mountain pass theorem to prove existence solution ...

In this paper, we study a class of quasilinear elliptic equations which appears in nonlinear optics. By using the mountain pass theorem together with technique adding one dimension space (Hirata et al. Topol Methods Nonlinear Anal 35:253–276, 2010; Jeanjean Theory Appl 28:1633–1659, 1997), prove existence non-trivial weak solution for general terms Berestycki–Lions’ type. The radial ground stat...

Abstract This work treats a typical type of quasilinear system concerning critical Sobolev growth. In the light Lions principle and Mountain pass lemma, mountain pass-type solutions can be derived.