The present paper is on the existence and behaviour of solutions for a class semilinear parabolic equations, defined bounded smooth domain assuming nonlinearity asymptotically linear at infinity. behavior when initial data varies in phase space analyzed. Global are obtained, which may be or blow-up infinite time (grow-up). main tools comparison principle variational methods. In particular, Neha...

In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, ensure the compactness embedding for weighted space into Orlicz spaces, provided weight is unbounded. We also obtain a version of Lions' “vanishing” Lemma by introducing new techniques overcome lack suitable interpolation law. Finally, as product results, use minimization method o...

We consider a non-local Shrödinger problem driven by the fractional Orlicz g-Laplace operator as follows(P)(−△g)αu+g(u)=K(x)f(x,u),inRd, where d≥3,(−△g)α is operator, f:Rd×R→R measurable function and K positive continuous function. Employing Nehari manifold method without assuming well-known Ambrosetti-Rabinowitz differentiability conditions on non-linear term f, we prove that (P) has ground st...

We study the existence of bound and ground states for a class nonlinear elliptic systems in RN. These equations involve critical power nonlinearities Hardy-type singular potentials, coupled by term containing up to powers. More precisely, we find if either positive coupling parameter ν is large or small under suitable assumptions on other parameters problem. Furthermore, are found as Mountain-P...

Abstract We investigate the relations between normalized critical points of nonlinear Schrödinger energy functional and corresponding action on associated Nehari manifold. Our first general result is that ground state levels are strongly related by following duality result: (negative) level Legendre–Fenchel transform level. Furthermore, whenever an exists at a certain frequency, then all states...

We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein (AAK) theorems. Among those generalizations: descriptions of Hankel operators in weighted 2 spaces; descriptions of Hankel operators from Dirichlet type spaces to weighted Bergman spaces; commutant ...

Abstract In this article, we investigate the Cauchy problem for Klein-Gordon equations with combined power-type nonlinearities. Coefficients in nonlinearities depend on space variable. They are sign preserving functions except one of coefficients, which may change its sign. We study completely structure Nehari manifold. By using potential well method, give necessary and sufficient conditions no...

We investigate the ground states for focusing, subcritical nonlinear Schrödinger equation with a point defect in dimension two, defined as minimizers of energy functional at fixed mass. prove that exist every positive mass and show logarithmic singularity defect. Moreover, up to multiplication by constant phase, they are positive, radially symmetric, decreasing along radial direction. In order ...