scholarly journals Singularly Perturbed Fractional Schrödinger Equation Involving a General Critical Nonlinearity

2018 ◽  
Vol 18 (3) ◽  
pp. 487-499 ◽  
Author(s):  
Hua Jin ◽  
Wenbin Liu ◽  
Jianjun Zhang
Keyword(s):  
Variational Approach ◽  
Bound State ◽  
Singularly Perturbed ◽  
Critical Nonlinearity ◽  
Bound State Solution ◽  
Critical Nonlinearities ◽  
Concentration Phenomena ◽  
Fractional Schrödinger Equations ◽  
Concentration Result ◽  
Made In

AbstractIn this paper, we are concerned with the existence and concentration phenomena of solutions for the following singularly perturbed fractional Schrödinger problem:\varepsilon^{2s}(-\Delta)^{s}u+V(x)u=f(u)\quad\text{in }\mathbb{R}^{N},where{N>2s}and the nonlinearityfhas critical growth. By using the variational approach, we construct a localized bound-state solution concentrating around an isolated component of the positive minimum point ofVas{\varepsilon\rightarrow 0}. Our result improves the study made in [X. He and W. Zou, Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities, Calc. Var. Partial Differential Equations 55 2016, 4, Article ID 91], in the sense that, in the present paper, theAmbrosetti–Rabinowitzcondition and themonotonicitycondition on{f(t)/t}are not required.

scholarly journals Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff-Type Problems with a General Critical Nonlinearity

2018 ◽  
Vol 61 (4) ◽  
pp. 1023-1040 ◽  
Author(s):  
Jianjun Zhang ◽  
David G. Costa ◽  
João Marcos do Ó
Keyword(s):  
Positive Solutions ◽  
Local Minimum ◽  
Type Equation ◽  
Bound State ◽  
State Solution ◽  
Critical Nonlinearity ◽  
Bound State Solution ◽  
Kirchhoff Type ◽  
Image Position ◽  
Kirchhoff Type Problems

AbstractWe are concerned with the following Kirchhoff-type equation$$ - \varepsilon ^2M\left( {\varepsilon ^{2 - N}\int_{{\open R}^N} {\vert \nabla u \vert^2{\rm d}x} } \right)\Delta u + V(x)u = f(u),\quad x \in {{\open R}^N},\quad N{\rm \ges }2,$$whereM ∈ C(ℝ+, ℝ+),V ∈ C(ℝN, ℝ+) andf(s) is of critical growth. In this paper, we construct a localized bound state solution concentrating at a local minimum ofVasε → 0 under certain conditions onf(s),MandV. In particular, the monotonicity off(s)/sand the Ambrosetti–Rabinowitz condition are not required.

New insight into the molecular switch mechanism of human Rho family proteins: shifting a paradigm

2013 ◽  
Vol 394 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Mamta Jaiswal ◽  
Eyad Kalawy Fansa ◽  
Radovan Dvorsky ◽  
Mohammad Reza Ahmadian
Keyword(s):  
Quantitative Analysis ◽  
Bound State ◽  
Molecular Switch ◽  
Nucleotide Exchange ◽  
Gtp Binding ◽  
Switch Mechanism ◽  
Rho Family ◽  
Rho Family Proteins ◽  
Insight Into ◽  
Made In

Abstract Major advances have been made in understanding the structure, function and regulation of the small GTP-binding proteins of the Rho family and their involvement in multiple cellular process and disorders. However, intrinsic nucleotide exchange and hydrolysis reactions, which are known to be fundamental to Rho family proteins, have been partially investigated in the case of RhoA, Rac1 and Cdc42, but for others not at all. Here we present a comprehensive and quantitative analysis of the molecular switch functions of 15 members of the Rho family that enabled us to propose an active GTP-bound state for the rather uncharacterized isoforms RhoD and Rif under equilibrium and quiescent conditions.

scholarly journals Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Eser Olğar ◽  
Hayder Dhahir ◽  
Haydar Mutaf
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Mass Function ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Bound State Solution ◽  
Function Generator ◽  
Dependent Mass ◽  
And Function ◽  
Position Dependent Mass

AbstractThe bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.

AB INITIO CALCULATION OF $^5_\Lambda {\rm He}$ WITH EXPLICIT Σ ADMIXTURE

2003 ◽  
Vol 18 (02n06) ◽  
pp. 139-142
Author(s):  
H. NEMURA ◽  
Y. AKAISHI ◽  
Y. SUZUKI
Keyword(s):  
Ab Initio ◽  
Internal Energy ◽  
Ab Initio Calculation ◽  
Degrees Of Freedom ◽  
Bound State ◽  
Bound State Solution ◽  
Expectation Value ◽  
Variational Calculations ◽  
Energy Expectation ◽  
Energy Expectation Value

Variational calculations for s-shell hypernuclei are performed by explicitly including Σ degrees of freedom. Two sets of YN interactions (D2 and SC97e(S)) are used. The bound-state solution of [Formula: see text] is obtained by using each of YN potentials, and a large energy expectation value of the tensor ΛN - ΣN transition part is found by using the SC97e(S). The internal energy of 4 He subsystem changes a lot by the presence of a Λ particle with the strong tensor ΛN - ΣN transition potential.

Existence of a bound state solution for quasilinear Schrödinger equations

2017 ◽  
Vol 8 (1) ◽  
pp. 323-338 ◽  
Author(s):  
Yan-Fang Xue ◽  
Chun-Lei Tang
Keyword(s):  
Nonlinear Term ◽  
Quasilinear Equation ◽  
Bound State ◽  
State Solution ◽  
Schrodinger Equations ◽  
Linking Theorem ◽  
Schrödinger Equations ◽  
Bound State Solution ◽  
Asymptotically Linear ◽  
Semilinear Equation

Abstract In this article, we establish the existence of bound state solutions for a class of quasilinear Schrödinger equations whose nonlinear term is asymptotically linear in {\mathbb{R}^{N}} . After changing the variables, the quasilinear equation becomes a semilinear equation, whose respective associated functional is well defined in {H^{1}(\mathbb{R}^{N})} . The proofs are based on the Pohozaev manifold and a linking theorem.

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