Abstract
We present new existence results for a family of nonconvex variational boundary-value problems. Our method is based on an argument that has already been used in such problems, although only in a very partial fashion. In order to be able to use the full strength of this argument, one is led to introduce technical hypotheses whose generality is not self-evident. Another component of this study is then to show that these hypotheses are actually generic, at least under sufficient smoothness of the data. There follows a generally calculable sufficient criterion for existence of solutions. What it really takes to go through the necessary calculations is illustrated by several examples. Closely related sufficient conditions to obtain uniqueness as well are also given.
Published Version
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