Bound-state solution in momentum space of three-particle equations with Coulomb interaction

1982 ◽  
Vol 32 (3) ◽  
pp. 311-315 ◽  
Author(s):  
L. P. Kok ◽  
H. van Haeringen
Keyword(s):  
Coulomb Interaction ◽  
Momentum Space ◽  
Bound State ◽  
State Solution ◽  
Bound State Solution

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.

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.

The existence and uniqueness of bound-state solutions of a semi-linear equation

2005 ◽  
Vol 461 (2061) ◽  
pp. 2941-2963 ◽  
Author(s):  
W.C Troy
Keyword(s):  
Linear Equation ◽  
Existence And Uniqueness ◽  
Bound States ◽  
Piecewise Linear ◽  
Bound State ◽  
State Solution ◽  
Bound State Solution ◽  
Real Zeros ◽  
Radially Symmetric Solutions ◽  
Solution Changes

We investigate the existence and uniqueness of bounded, radially symmetric solutions in R 3 of Δ u + f ( u )=0, where f ( u ) is continuous, piecewise linear, and has three distinct real zeros. We give a detailed construction of the first two bound states which satisfy as r →∞. The first is the well known positive bound-state solution. The second solution changes sign and has exactly one zero in (0,∞). We prove that both of these solutions are unique.

The jost function and bound state solution for the hulthén potential

1975 ◽  
Vol 239 (1) ◽  
pp. 89-92 ◽  
Author(s):  
B. Talukdar ◽  
M.N. Sinha Roy ◽  
D. Chattarji
Keyword(s):  
Bound State ◽  
State Solution ◽  
Bound State Solution ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Jost Function

Approximate and analytical bound state solutions of the Frost–Musulin potential

2014 ◽  
Vol 92 (1) ◽  
pp. 18-21 ◽  
Author(s):  
A.G. Adepoju ◽  
E.J. Eweh
Keyword(s):  
Functional Analysis ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Short Range ◽  
Bound State ◽  
State Solution ◽  
Centrifugal Term ◽  
Analysis Method ◽  
Bound State Solution ◽  
Short Range Potential

Despite all the attempts made by several authors to investigate the bound state solutions of the Schrödinger equation with various potentials, until now, such investigations have not been conducted for Frost–Musulin diatomic potential. In this study, we obtain the approximate bound state solution of this potential via the functional analysis method. We also numerically solved the Schrödinger equation without any approximation to centrifugal term for the same potential. The comparisons between the results reveal the accuracy of our approximate results for short-range potential.

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