@article {DEMARCHIS20102165, title = {Generic multiplicity for a scalar field equation on compact surfaces}, journal = {Journal of Functional Analysis}, volume = {259}, number = {8}, year = {2010}, pages = {2165 - 2192}, abstract = {

We prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

}, keywords = {Generic multiplicity, Geometric PDE{\textquoteright}s, Morse inequalities, Scalar field equations}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2010.07.003}, url = {http://www.sciencedirect.com/science/article/pii/S0022123610002697}, author = {Francesca De Marchis} }