The structure of nontrivial nonnegative solutions to singularly perturbed quasilinear Dirichlet problems of the form It is shown that there are many nontrivial nonnegative solutions with spike-layers. Moreover, the measure of each spike-layer is estimated as β 0 + . These results are applied to the
Spike-layered solutions of singularly perturbed quasilinear Dirichlet problems
β Scribed by Zhengce Zhang; Kaitai Li
- Book ID
- 108345288
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 143 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0022-247X
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## Abstract We study structure of nontrivial nonnegative solutions for a class of singularly perturbed quasilinear Dirichlet problems. It is shown that there are infinitely many leastβenergy solutions and they are spikeβlayer solutions. Moreover, the measure of each spikeβlayer is estimated as the
By means of a penalization scheme due to del Pino and Felmer, we prove the existence of single-peaked solutions for a class of singularly perturbed quasilinear elliptic equations associated with functionals which lack of smoothness. We do not require neither uniqueness assumptions on the limiting au