Multiple solutions for a class of semilinear elliptic problems with Robin boundary condition

AbstractIn this paper, we show the existence of at least four nontrivial solutions for a class of semilinear elliptic problems with Robin boundary condition and jumping nonlinearities. Solvability of oscillating equations with Robin boundary condition is also investigated. We prove the conclusions by using sub-super-solution method, Fučík spectrum theory, mountain pass theorem in order intervals and Morse theory

Asymptotics for a dissipative dynamical system with linear and gradient-driven damping

We study, in the setting of a real Hilbert space H, the asymptotic behavior of trajectories of the second-order dissipative dynamical system with linear and gradient-driven nonlinear damping where λ > 0 and f, Φ: H → R are two convex differentiable functions. It is proved that if Φ is coercive and bounded from below, then the trajectory converges weakly towards a minimizer of Φ. In particular, we state that under suitable conditions, the trajectory strongly converges to the minimizer of Φ exponentially or polynomially

Degree Distribution of Arbitrary AANET

Taking the safe distance between two adjacent planes in the same airline into account, we give a model for the multiairline aeronautical ad hoc network (AANET). Based on our model, we analyze the plane’s degree distribution of any arbitrary AANET. Then, the expressions of the degree distributions of one single plane and the whole networks are both worked out and verified by the simulations, in which we generate several random AANETs. Since our model is a reasonable abstraction of the real situation, the theoretical result we get is very close to the result of the real networks, which is also shown in the simulations

Support Vector Regression Method for Wind Speed Prediction Incorporating Probability Prior Knowledge

Prior knowledge, such as wind speed probability distribution based on historical data and the wind speed fluctuation between the maximal value and the minimal value in a certain period of time, provides much more information about the wind speed, so it is necessary to incorporate it into the wind speed prediction. First, a method of estimating wind speed probability distribution based on historical data is proposed based on Bernoulli’s law of large numbers. Second, in order to describe the wind speed fluctuation between the maximal value and the minimal value in a certain period of time, the probability distribution estimated by the proposed method is incorporated into the training data and the testing data. Third, a support vector regression model for wind speed prediction is proposed based on standard support vector regression. At last, experiments predicting the wind speed in a certain wind farm show that the proposed method is feasible and effective and the model’s running time and prediction errors can meet the needs of wind speed prediction