On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function

By Tsung‐fang Wu. 2006

222 citations recorded by the source corpus.

Abstract In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign-changing weight function. With the help of the Nehari manifold, we prove that there are at least two positive solutions for Eq. ( E λ , f ) in bounded domains.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ce73fc28cfb8f6ef868af9b547618f95f722b3fd

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions (2011, background): “[19], Brown-Wu [7, 8] and Wu [29, 30]; in particular, the existence of at least two positive solutions has been demonstrated in [7, 8, 29, 30] with the nonlinearity given by λ f(x) |u| q−2 u+ g(x) |u| p−2 u.”
The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions (2008, methodology): “For more general cases, we refer the reader to Ambrosetti–Azorezo–Peral [2], de Figueiredo–Gossez–Ubilla [9], EL Hamidi [10] and Wu [17, 18], etc.”
The Nehari manifold for fractional systems involving critical nonlinearities (2015, background): “1) for the Laplacian operator have been studied extensively in recent years, see [1, 13, 19, 20, 30, 31] and the references therein.”
Multiplicity Results for a Semi-Linear Elliptic Equation Involving Sign-Changing Weight Function (2009, background): “Wu [8] proved that equation (Ea,b) has at least two positive solutions under the assumptions the weight functions a change sign in Ω, b ≡ 1 and λ is sufficiently small.”