We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. The functionals considered belong to a class which includes semi-coercive, compact-coercive and P-coercive functionals. Some applications to nonlinear partial differential equations are given.
We consider the eigenvalue problem in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all are eigenvalues.
We consider the eigenvalue problem in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all λ > 0 are eigenvalues.
The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.
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