It turns out that p = 2 is a critical value for the existence of solutions.doi:10.1016/j.jfa.2006.04.005David RuizElsevier Inc.Journal of Functional AnalysisD. Ruiz, The Schr¨odinger-Poisson equation under the effect of a nonlinear local term, J. Functional Analysis, 237(2006), 655-674...
[sol,fval,exitflag,output,lambda] = solve(___)also returns an exit flag describing the exit condition, anoutputstructure containing additional information about the solution process, and, for non-integer optimization problems, a Lagrange multiplier structure. example Examples collapse all Solve Linear...
It then becomes natural to also consider the case g(p) = ∂tp, in which case the Lagrange multiplier satisfies a wave equation and the generalised Maxwell's equations become hyperbolic and even strictly hyperbolic if a Lagrange multiplier is also used for the div B constraint. This set of...
Active field theories, such as the paradigmatic model known as ‘active model B+’, are simple yet very powerful tools for describing phenomena such as motility-induced phase separation. No comparable theory has been derived yet for the underdamped case.
Given a nonlinearityand set, we are interested to seek for multiple solutionsof the nonlocal equation (1.1) where,andis the Riesz potential defined by heredenotes the space of radially symmetric Sobolev functions. We aim to analyze the two cases:is a fixed positive constant oris unknown and th...
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Theorem 1.1 generalizes the result by Burq, Gérard and Tzvetkov from [7], Theorem 3, for the cubic NLS to the stochastic setting. Note that this uniqueness result holds for both the focusing and defocusing case. Combining Theorem 1.1 with the existence of martingale solutions proved by the ...
The next section of this chapter shows how these relationships can be transformed into algebraic functions even if they contain calculus operators, at least for sinusoidal signals. If the transfer function is an algebraic multiplier, then when two systems are connected in series, as in Figure 5.4...
where a is the slope and b is the intercept. Often, the height term is expressed as the difference from a reference value such as height in inches in excess of 5 ft. For example, the sex-specific equations of Hamwi (3), which were developed for the US system, estimate IBW for men...
This repo is to hold the public dataset for EquationGPT, which aims to collect Equation related Q&A corpus to finetune foundation models of GPT/ChatGPT. Each prompt-completion pairs contains information about the latex code for the equation, the meaning of each symbols, and related materials. ...