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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
Using the variational method, we obtain that there exists a positive constant λ∗ > 0 such that for all λ ∈ 0, λ∗ , the system has at least two positive solutions.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this paper, we study the following critical growth Schr¨odinger–Poisson system with concave-convex nonlinearities term { −∆u + u + ηφu = λf x u q−1 + u 5 , in R 3 , −∆φ = u 2 , in R 3 , 0.1 where 1 0 is a real parameter and f ∈ L 6 6−q R 3 is a nonzero nonnegative function.
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Temel Bulgular & Veri:In this paper, we study the following critical growth Schr¨odinger–Poisson system with concave-convex nonlinearities term { −∆u + u + ηφu = λf x u q−1 + u 5 , in R 3 , −∆φ = u 2 , in R 3 , 0.1 where 1 0 is a real parameter and f ∈ L 6 6−q R 3 is a nonzero nonnegative function.
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Sonuç & Katkı:Using the variational method, we obtain that there exists a positive constant λ∗ > 0 such that for all λ ∈ 0, λ∗ , the system has at least two positive solutions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Schrödinger-Poisson system · critical exponent · concave-convex nonlinearities
Abstract
In this paper, we study the following critical growth Schr¨odinger–Poisson system with concave-convex nonlinearities term { −∆u + u + ηφu = λf x u q−1 + u 5 , in R 3 , −∆φ = u 2 , in R 3 , 0.1 where 1 0 is a real parameter and f ∈ L 6 6−q R 3 is a nonzero nonnegative function. Using the variational method, we obtain that there exists a positive constant λ∗ > 0 such that for all λ ∈ 0, λ∗ , the system has at least two positive solutions.
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Bu Makaleye Atıf Yap
LEI, C., LIU, G., CHU, C., SUO, H. (2020). New multiple solutions for a Schrödinger-Poisson system involving concave-convex nonlinearities. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 3, 986–997. https://ajindex.com/articles/193197