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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.6686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-28T18:05:37Z","cross_cats_sorted":[],"title_canon_sha256":"16c56b20386c5e2f978e3dc814ab921010ec83649a23ecd36682d9c1ba8555ed","abstract_canon_sha256":"6d5c0f6f67e1bf57e8fcf4632af4f59837702d2c852d3700a54cebc89d661b28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:58.539029Z","signature_b64":"J3H1e+TNif0DsJK3xpbeUvhtOzo8XUJDEFZU8zxsYzG2p3ZaHpSj4y2tKgcyIoEaxJ+5HXITuu8QOM02TEJZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db17ddf9b40b4945eaaec00c0179bae4377d35dcec35ff5b492f520f18c41b13","last_reissued_at":"2026-05-18T02:18:58.538334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:58.538334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $f(u)=|u|^{p-1}u$. 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