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Multiple Solutions

In: Linking Methods in Critical Point Theory

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  • Martin Schechter

    (University of California, Department of Mathematics)

Abstract

There are various tools that one can use in critical point theory to show that G’(u) = 0 has multiple solutions. One of them is to solve 10.1.1 $$G\left( u \right) = c,G'\left( u \right) = 0$$ for different values of c. We have used this device several times, especially when we verified that a solution was not trivial. In this chapter we shall use another method which helps us locate a region in Hilbert space where a particular solution is stuated. If we find a solution in another region we are sure that we have another solution. This process can be repeated. We present the theory in the next section and give applications in Section 10.3.

Suggested Citation

  • Martin Schechter, 1999. "Multiple Solutions," Springer Books, in: Linking Methods in Critical Point Theory, chapter 0, pages 219-228, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1596-7_10
    DOI: 10.1007/978-1-4612-1596-7_10
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