2,334 research outputs found
Multiple positive solutions of a Sturm-Liouville boundary value problem with conflicting nonlinearities
We study the second order nonlinear differential equation \begin{equation*}
u"+ \sum_{i=1}^{m} \alpha_{i} a_{i}(x)g_{i}(u) - \sum_{j=0}^{m+1} \beta_{j}
b_{j}(x)k_{j}(u) = 0, \end{equation*} where ,
are non-negative Lebesgue integrable functions defined in
, and the nonlinearities are
continuous, positive and satisfy suitable growth conditions, as to cover the
classical superlinear equation , with . When the positive
parameters are sufficiently large, we prove the existence of at
least positive solutions for the Sturm-Liouville boundary value
problems associated with the equation. The proof is based on the Leray-Schauder
topological degree for locally compact operators on open and possibly unbounded
sets. Finally, we deal with radially symmetric positive solutions for the
Dirichlet problems associated with elliptic PDEs.Comment: 23 pages, 6 PNG figure
Multiple positive solutions for a superlinear problem: a topological approach
We study the multiplicity of positive solutions for a two-point boundary
value problem associated to the nonlinear second order equation .
We allow to change its sign in order to cover the case of
scalar equations with indefinite weight. Roughly speaking, our main assumptions
require that is below as and above
as . In particular, we can deal with the situation
in which has a superlinear growth at zero and at infinity. We propose
a new approach based on the topological degree which provides the multiplicity
of solutions. Applications are given for , where we prove
the existence of positive solutions when has positive
humps and is sufficiently large.Comment: 36 pages, 3 PNG figure
Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems
We prove the existence of positive periodic solutions for the second order
nonlinear equation , where has superlinear growth at
zero and at infinity. The weight function is allowed to change its sign.
Necessary and sufficient conditions for the existence of nontrivial solutions
are obtained. The proof is based on Mawhin's coincidence degree and applies
also to Neumann boundary conditions. Applications are given to the search of
positive solutions for a nonlinear PDE in annular domains and for a periodic
problem associated to a non-Hamiltonian equation.Comment: 41 page
Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case
We study the periodic and the Neumann boundary value problems associated with
the second order nonlinear differential equation \begin{equation*} u'' + c u' +
\lambda a(t) g(u) = 0, \end{equation*} where is a
sublinear function at infinity having superlinear growth at zero. We prove the
existence of two positive solutions when and
is sufficiently large. Our approach is based on Mawhin's
coincidence degree theory and index computations.Comment: 26 page
Evaluating distributed generation impacts with a multiobjective index
Evaluating the technical impacts associated with connecting distributed generation to distribution networks is a complex activity requiring a wide range of network operational and security effects to be qualified and quantified. One means of dealing with such complexity is through the use of indices that indicate the benefit or otherwise of connections at a given location and which could be used to shape the nature of the contract between the utility and distributed generator. This paper presents a multiobjective performance index for distribution networks with distributed generation which considers a wide range of technical issues. Distributed generation is extensively located and sized within the IEEE-34 test feeder, wherein the multiobjective performance index is computed for each configuration. The results are presented and discussed
Evaluating Distributed Time-Varying Generation Through a Multiobjective Index
In the last decade, distributed generation, with its various technologies, has increased its presence in the energy mix presenting distribution networks with challenges in terms of evaluating the technical impacts that require a wide range of network operational effects to be qualified and quantified. The inherent time-varying behavior of demand and distributed generation (particularly when renewable sources are used), need to be taken into account since considering critical scenarios of loading and generation may mask the impacts. One means of dealing with such complexity is through the use of indices that indicate the benefit or otherwise of connections at a given location and for a given horizon. This paper presents a multiobjective performance index for distribution networks with time-varying distributed generation which consider a number of technical issues. The approach has been applied to a medium voltage distribution network considering hourly demand and wind speeds. Results show that this proposal has a better response to the natural behavior of loads and generation than solely considering a single operation scenario
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