Search results for "Nonlinear system"
showing 10 items of 1446 documents
Well-posed nonlinear problems in integrated circuits modeling
1991
In this paper we study the problem (E) + (BC) + (IC) (see below) which represents a model for integrated circuits. We assume that the distributed parametersr(x) andc(x) are nonconstant, dielectric leakages depend on thex-coordinate as well as the voltage level, while the interconnecting multiport is nonlinear and possibly multivalued.
Batch fermentation process: Modelling and direct sensitivity analysis
2009
Based on a nonlinear model, this article realizes an investigation of dynamic behaviour of a batch fermentation process using direct sensitivity analysis (DSA). The used nonlinear mathematical model has a good qualitative and quantitative description of the alcoholic fermentation process. This model has been discussed and validated by authors in other studies. The DSA of dynamic model was used to calculate the matrix of the sensitivity functions in order to determine the influence of the small deviations of initial state, control inputs, and parameters from the ideal nominal values on the state trajectory and system output in time. Process optimization and advanced control strategies can be…
(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms
2018
We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian ($$p>2$$) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric $$(p-1)$$-linear term which is resonant as $$x \rightarrow - \infty $$, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.
Triple solutions for nonlinear elliptic problems driven by a non-homogeneous operator
2020
Abstract Some multiplicity results for a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of p -Laplacian type are given. Via variational methods, the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and/or nonlinear terms satisfying different asymptotic conditions.
Positive solutions for singular (p, 2)-equations
2019
We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.
An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities
2005
AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.
Multiple solutions for a Dirichlet problem with p-Laplacian and set-valued nonlinearity
2008
AbstractThe existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via sub- and supersolution methods as well as variational techniques for nonsmooth functions.
Elliptic problems with convection terms in Orlicz spaces
2021
Abstract The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.
Radial solutions of Dirichlet problems with concave-convex nonlinearities
2011
Abstract We prove the existence of a double infinite sequence of radial solutions for a Dirichlet concave–convex problem associated with an elliptic equation in a ball of R n . We are interested in relaxing the classical positivity condition on the weights, by allowing the weights to vanish. The idea is to develop a topological method and to use the concept of rotation number. The solutions are characterized by their nodal properties.
Nonlinear Potential Theory and PDEs
1994
We consider equations like — div(∣∇u∣ p-2∇u) = µ, where µ is a nonnegative Radon measure and 1 < p < ∞. Results that relate the solution u and the measure µ are reviewed. A link between potential estimates and the boundary regularity of the Dirichlet problem is established.