This article concerns the existence of solutions to Schrodinger-Poisson system $$\displaylines{ -\Delta_p u+|u|^{p-2}u+\lambda\phi u=|u|^{q-2}u+h(x) \quad \hbox{in }\mathbb{R}^3,\\ -\Delta \phi=u^2 }\mathbb{R}^3, }$$ where \( 4/3 < p 12/5 \), q p^{*}=3p/(3-p) \(\Delta_p u =\hbox{div}(|\nabla u|^{p-2}\nabla u)\), \(\lambda >0\), and \(h \not= 0\). The multiplicity results are obtained by u...

In the present paper we deal with a quasilinear problem involving singular term and parametric superlinear perturbation. We are interested in existence, nonexistence multiplicity of positive solutions as parameter λ > 0 ...

Let X be a real Banach space and Φ ∈ C 1 (X, R) a function with a mountain pass geometry. This ensures the existence of a Palais-Smale, and even a Cerami, sequence {u n } of approximate critical points for the mountain pass level. We obtain information about the location of such a sequence by estimating the distance of u n from S for certain types of set S as n → ∞. Under our hypotheses we can ...

The concentration compactness framework for semilinear elliptic equations without compactness, set originally by P.-L.Lions for constrained minimization in the case of homogeneous nonlinearity, is extended here to the case of general nonlinearities in the standard mountain pass setting of Ambrosetti–Rabinowitz. In these setting, existence of solutions at the mountain pass level c is verified un...

First, we show the equivalence of two definitions left Riemann–Liouville fractional integral on time scales. Then, establish and characterize Sobolev space with help notion derivative At same time, define weak derivatives demonstrate that they coincide ones Next, prove kinds norms in introduced derive its completeness, reflexivity, separability, some embedding. Finally, as an application, by co...

In this paper, we consider the nonlinear impulsive generalized fractional differential equations with (p,q)-Laplacian operator for 1<p≤q<∞, in which nonlinearity f contains two derivatives respect to another function. Since complexity of term and impulses exist calculus, it is difficult find corresponding variational functional problem. The existence nontrivial solutions problem establish...

In this paper, we consider a neutral molecule that possesses two distinct stable positions for its nuclei, and look for a mountain pass point between the two minima in the non-relativistic Schrödinger framework. We first prove some properties concerning the spectrum and the eigenstates of a molecule that splits into pieces, a behaviour which is observed when the Palais-Smale sequences obtained ...

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.