An Introduction to Minimax Theorems and Their Applications by Maria do Rosário Grossinho, Stepan Agop Tersian

By Maria do Rosário Grossinho, Stepan Agop Tersian

The ebook is meant to be an creation to severe element concept and its functions to differential equations. even supposing the similar fabric are available in different books, the authors of this quantity have had the subsequent objectives in brain:

  • to provide a survey of latest minimax theorems,
  • to offer functions to elliptic differential equations in bounded domain names,
  • to contemplate the twin variational technique for issues of non-stop and discontinuous nonlinearities,
  • to provide a few parts of severe aspect concept for in the community Lipschitz functionals and provides functions to fourth-order differential equations with discontinuous nonlinearities,
  • to check homoclinic options of differential equations through the variational equipment.

The contents of the ebook encompass seven chapters, every one divided into numerous sections.
Audience: Graduate and post-graduate scholars in addition to experts within the fields of differential equations, variational tools and optimization.

Show description

Read or Download An Introduction to Minimax Theorems and Their Applications to Differential Equations PDF

Best linear programming books

Classes of linear operators

This e-book offers a landscape of operator conception. It treats quite a few periods of linear operators which illustrate the richness of the idea, either in its theoretical advancements and its purposes. for every of the periods numerous differential and necessary operators encourage or illustrate the most effects.

Basic Classes of Linear Operators

A comprehensive graduate textbook that introduces functional research with an emphasis at the idea of linear operators and its software to differential equations, critical equations, endless platforms of linear equations, approximation conception, and numerical research. As a textbook designed for senior undergraduate and graduate scholars, it starts off with the geometry of Hilbert areas and proceeds to the idea of linear operators on those areas together with Banach areas.

Time Continuity in Discrete Time Models: New Approaches for Production Planning in Process Industries (Lecture Notes in Economics and Mathematical Systems)

Creation making plans difficulties containing designated features from technique industries are addressed during this ebook. the most topic is the improvement of mathematical programming versions that let to version creation plans which aren't disrupted via discretization of time. despite the fact that, discrete time versions are used as a foundation and are hence stronger to incorporate points of time continuity.

Additional resources for An Introduction to Minimax Theorems and Their Applications to Differential Equations

Example text

17. Let c E R, p > and fECI (E, R) be a functional. Suppose that f satisfies (PS)~ condition and N is a neighborhood of Kc. Then there exist EO > 0, nO E N and a f -decreasing homotopy of homeomorphisms 'fin : [0, 1] X En -7 En for n (1) (2) (3) ~ no such that if 10 E (0, EO) 'fin (t, u) = u if either u E K~ or If (u) - cl ~ 'fin (1, (fc+E\N) n En) C f C - E, II'fin (t,u) - ulln:S; p, V(t,u) E [0,1] X En· 210, Proof. The condition (PS)~ implies the existence of {3 > 0, EO > 0, 8 E (0, p/2) and no such that if n ~ no and If (u) - cl :s; EO, then u E (En \N)28 Ilf~ (u)1In ~ {3.

17. Let c E R, p > and fECI (E, R) be a functional. Suppose that f satisfies (PS)~ condition and N is a neighborhood of Kc. Then there exist EO > 0, nO E N and a f -decreasing homotopy of homeomorphisms 'fin : [0, 1] X En -7 En for n (1) (2) (3) ~ no such that if 10 E (0, EO) 'fin (t, u) = u if either u E K~ or If (u) - cl ~ 'fin (1, (fc+E\N) n En) C f C - E, II'fin (t,u) - ulln:S; p, V(t,u) E [0,1] X En· 210, Proof. The condition (PS)~ implies the existence of {3 > 0, EO > 0, 8 E (0, p/2) and no such that if n ~ no and If (u) - cl :s; EO, then u E (En \N)28 Ilf~ (u)1In ~ {3.

14. Suppose that fECI (X, R) satisfies (PS)c,cp condition for a given c E Rand

. Let N = K c,40 be a neighborhood of Kc. Then there exist c > 0 and a f -decreasing homotopy of homeomorphisms ", : [0,1] x X -+ X such that: (1) ", (t, x) = x if x E Kc or If (x) - cl ~ 2c, E. (2) ", (1, fC+E\N) c r- Proof. The set N is bounded because Kc (J) is compact by (PS)c,cp condition. Let Ro be such that NCB Ro. 33) 11/ (Xj) I < y. By (PS)c,cp condition (Xj)j has a convergent subsequence, which is a contradiction to limj Ilxjll = 00.

Download PDF sample

Rated 4.04 of 5 – based on 11 votes