Li and Song demonstrate how variational methods can be used in nonlinear differential equations, but begin by reviewing prerequisites such as Sobolev space and the variational principle for readers who are a little rusty. The other topics are quasilinear fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. Except for references to the basic results in the first chapter, each chapter is essentially a stand-alone entity that can be read with little reference to the other chapters. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)
Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis).In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included.
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