A variational approach to some boundary value problems in the half-line

We study the existence of solutions for two kinds of boundary value problem in the interval [0, (infinity) [. The problems are suggested by models in Mathematical Physics. In the first kind of problem the condition at the left endpoint is u(0) = a while in the second kind a homogeneous Neumann condi...

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Published in:Zeitschrift für angewandte Mathematik und Physik 2005-03, Vol.56 (2), p.192-209
Main Authors: Gomes, J. M., Sanchez, L.
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description We study the existence of solutions for two kinds of boundary value problem in the interval [0, (infinity) [. The problems are suggested by models in Mathematical Physics. In the first kind of problem the condition at the left endpoint is u(0) = a while in the second kind a homogeneous Neumann condition u'(0) = 0 is imposed. In both cases solutions should satisfy u(-I-(infinity)) = 0. Our approach is variational, solutions being obtained as minimizers or mountain pass critical points of some functional.
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