Schrödinger equations
Existence results for the general Schrödinger equations with a superlinear Neumann boundary value problem
... general Schrödinger equations with a superlinear Neumann boundary value problem in domains with conical points on the boundary of the ...the equations are given, and then the existence result of ...
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Lie Symmetries of Klein Gordon and Schrödinger Equations
... and Schrödinger equations are mainly two necessary equations, so it is compulsory that we can apply these eq- uations and resolve their Lie point symmetries in the direction of discovering their ...
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Existence of Ordered Solutions to Quasilinear Schrödinger Equations with General Nonlinear Term
... In recent years, studies about the nontrivial solutions of Schrödinger equations are very popular, involving differential equations, linear algebra and many sub- jects. The solution of these problems ...
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Ground state solution and multiple solutions to asymptotically linear Schrödinger equations
... on the existence of a ground state solution in the asymptotically linear case. Motivated by [], this paper is to present a different approach involving the critical point theory with the discreteness property of the ...
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Existence of solutions for a class of quasilinear Schrödinger equations on \({\mathbb{R}}\)
... In this paper, we study the existence of nontrivial solution for a class of quasilinear Schrödinger equations in R with the nonlinearity asymptotically linear and, furthermore, the potential indefinite in ...
5
Positive solutions for a class of quasilinear Schrödinger equations with vanishing potentials
... matter []. Equation (.) also appears in plasma physics and fluid mechanics [] and in dissipative quantum mechanics []. While this paper deals with the model where l(s) = s and we put z(t, x) = exp(–iEt)u(x) into ...
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Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions
... Using variational methods, we study the existence and multiplicity of homoclinic solutions for a class of discrete Schrödinger equations in infinite m-dimensional lattices with nonlinearities being ...
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Existence and multiplicity of positive bound states for Schrödinger equations
... Because of the important background in nonlinear optics and other fields, many authors pay more attention to the study of different types of vector nonlinear Schrödinger equa- tions, we refer the readers to [–]. ...
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Multiple solutions to nonlinear Schrödinger equations with critical growth
... In 2000, Cingolani and Lazzo (J. Differ. Equ. 160:118-138, 2000) studied nonlinear Schrödinger equations with competing potential functions and considered only the subcritical growth. They related the number ...
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Computational Methods for Three Coupled Nonlinear Schrödinger Equations
... obtained and novel shape changing in elastic collision property has been brought out. The system for N = 3 is of physical interest, in optical communication, and in bio- physics this system can be used to study the ...
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Multiple solutions of discrete Schrödinger equations with growing potentials
... nonlinear Schrödinger equation is one of the most important discrete mod- els, which plays an important role in many fields; for example, in biomolecular chains [], nonlinear optics [], Bose-Einstein condensates ...
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Multiplicity of solutions for fractional Schrödinger equations with perturbation
... there were also many works; see [–]. The fractional Schrödinger equation is a fun- damental equation of fractional quantum mechanics. The fractional quantum mechanics has been discovered as a result of ...
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A Schrödinger type algorithm for solving the Schrödinger equations via Phragmén–Lindelöf inequalities
... smooth equations, and a Schrödinger-type method is proposed to solve it iteratively so that a solution of the system of the Schrödinger equations is ...the Schrödinger type ...
14
Radial sign-changing solutions to biharmonic nonlinear Schrödinger equations
... In this work we obtain three radial solutions of a biharmonic stationary Schrödinger equation, one being positive, one negative, and one sign changing. The dual decomposition method is used to split the natural ...
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Time-local unraveling of non-Markovian stochastic Schrödinger equations
... odinger equations can be efficiently computed numerically, justifying their wide use in the three aforementioned ...odinger equations as averages over the solutions of time-local stochastic Schr¨ odinger ...
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On Coupled Klein-Gordon-Schrödinger Equations with Acoustic Boundary Conditions
... given functions. We will denote by ν the unit outward normal vector to Γ. Δ stands for the Laplacian with respect to the spatial variables; ’ denotes the derivative with respect to time t. Here zx, t is the normal ...
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Global well-posedness for nonlinear fourth-order Schrödinger equations
... theory and Strichartz-type estimates, but the sharp conditions of the global existence and blow up for the problem by potential well theory is still not considered for μ = . In this paper we try to solve this problem by ...
8
Including Arbitrary Geometric Correlations into One-Dimensional Time-Dependent Schrödinger Equations
... An example of the practical utility of the SSE, a Monte Carlo simulation scheme to describe quantum electron transport in open systems that is valid both for Markovian or non-Markovian regimes and that guarantees a ...
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Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations
... We start with a short Section 2 fixing some general notations that are used throughout the paper. In Section 3, we discuss a toy model with ”unphysical” Hamiltonian ε(p) = −p. The toy model is discussed from other point ...
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Schrödinger equations in noncylindrical domains: exact controllability
... [7] J.-L. Lions, Probl`emes aux Limites dans Les ´ Equations aux D´eriv´ees Partielles, Deuxi`eme ´edition. S´eminaire de Math´ematiques Sup´erieures, no. 1 ( ´Et´e, 1962), Les Presses de l’Universit´e de ...
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