{"paper":{"title":"An energy constrained method for the existence of layered type solutions of NLS equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Alessio, Piero Montecchiari","submitted_at":"2012-11-28T18:05:37Z","abstract_excerpt":"We study the existence of positive solutions on $\\R^{N+1}$ to semilinear elliptic equation $-\\Delta u+u=f(u)$ where $N\\geq 1$ and $f$ is modeled on the power case $f(u)=|u|^{p-1}u$. Denoting with $c$ the mountain pass level of $\\f(u)=\\tfrac 12\\|u\\|^{2}_{H^{1}(\\R^{N})}-\\int_{\\R^{N}}F(u)\\, dx$, $u\\in H^{1}(\\R^{N})$ ($F(s)=\\int_{0}^{s}f(t)\\, dt$), we show, via a new energy constrained variational argument, that for any $b\\in [0,c)$ there exists a positive bounded solution $v_{b}\\in C^{2}(\\R^{N+1})$ such that $E_{v_{b}}(y)=\\tfrac 12\\|\\partial_{y}v_{b}(\\cdot,y)\\|^{2}_{L^{2}(\\R^{N})}-V(v_{b}(\\cdot,y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6686","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}