Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical points with prescribed energy for a class of functionals
  depending on a parameter: existence, multiplicity and bifurcation results   We look for critical points with prescribed energy for the family of even
functionals $\Phi_\mu=I_1-\mu I_2$, where $I_1,I_2$ are $C^1$ functionals on a
Banach space $X$, and $\mu \in \mathbb{R}$. For several classes of $\Phi_\mu$
we prove the existence of infinitely many couples $(\mu_{n,c}, u_{n,c})$ such
that $$\Phi'_{\mu_{n,c}}(\pm u_{n,c}) = 0 \quad \mbox{and} \quad
\Phi_{\mu_{n,c}}( \pm u_{n,c}) = c \quad \forall n \in \mathbb{N}.$$ More
generally, we analyze the structure of the solution set of the problem
$$\Phi_\mu'(u)=0, \quad \Phi_{\mu}(u)=c$$ with respect to $\mu$ and $c$. In
particular, we show that the maps $c \mapsto \mu_{n,c}$ are continuous, which
gives rise to a family of {\it energy curves} for this problem. The analysis of
these curves provide us with several bifurcation and multiplicity type results,
which are then applied to some elliptic problems. Our approach is based on the
{\it nonlinear generalized Rayleigh quotient} method developed in \cite{I1}.

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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph