The existence of classical solutions to a one-dimensional non-linear fourth-order elliptic equation arising in quantum semiconductor modeling is proved for a class of non-homogeneous boundary conditions using degree theory. Furthermore, some non-existence results for other classes of boundary conditions are presented.
L'existence des solutions classiques pour une équation élliptique non-linéaire d'ordre quatre en une dimension, qui apparaît dans la modélisation des semi-conducteurs quantiques, est démontrée pour une classe de conditions aux limites non-homogènes en utilisant la théorie du degré. En plus, des résultats de non-existence pour d'autres classes de conditions aux limites sont établis.
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Pablo Amster 1; Ansgar Jüngel 2; Daniel Matthes 3
@article{CRMATH_2008__346_3-4_143_0, author = {Pablo Amster and Ansgar J\"ungel and Daniel Matthes}, title = {Non-homogeneous boundary conditions for a fourth-order diffusion equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {143--148}, publisher = {Elsevier}, volume = {346}, number = {3-4}, year = {2008}, doi = {10.1016/j.crma.2007.12.001}, language = {en}, }
TY - JOUR AU - Pablo Amster AU - Ansgar Jüngel AU - Daniel Matthes TI - Non-homogeneous boundary conditions for a fourth-order diffusion equation JO - Comptes Rendus. Mathématique PY - 2008 SP - 143 EP - 148 VL - 346 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2007.12.001 LA - en ID - CRMATH_2008__346_3-4_143_0 ER -
Pablo Amster; Ansgar Jüngel; Daniel Matthes. Non-homogeneous boundary conditions for a fourth-order diffusion equation. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 143-148. doi : 10.1016/j.crma.2007.12.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.12.001/
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