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Volume 26, Issue 1
Ground State Solutions for a Semilinear Elliptic Equation Involving Concave-convex Nonlinearities

O. Khazaee Kohpar & Somayeh Khademloo

DOI: 10.4208/jpde.v26.n1.2

J. Part. Diff. Eq., 26 (2013), pp. 14-24.

Published online: 2013-03

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  • Abstract

This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem $-Δu=λa(x)u|u|^{q-2}+ b(x)u|u|^{2^∗-2}$ in a bounded domain coupled with Dirichlet boundary condition. Here $2^∗$ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions. Using the Nehari manifold method we prove that one can find an interval L such that there exist at least two positive solutions of the problem for $λ∈Λ$.

  • Keywords

Semilinear elliptic equations Nehari manifold concave-convex nonlinearities

  • AMS Subject Headings

35J25, 35J20, 35J61

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

kolsoomkhazaee@yahoo.com (O. Khazaee Kohpar)

s.khademloo@nit.ac.ir (Somayeh Khademloo)

  • BibTex
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  • TXT
@Article{JPDE-26-14, author = {Khazaee Kohpar , O. and Khademloo , Somayeh}, title = {Ground State Solutions for a Semilinear Elliptic Equation Involving Concave-convex Nonlinearities}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {1}, pages = {14--24}, abstract = {

This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem $-Δu=λa(x)u|u|^{q-2}+ b(x)u|u|^{2^∗-2}$ in a bounded domain coupled with Dirichlet boundary condition. Here $2^∗$ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions. Using the Nehari manifold method we prove that one can find an interval L such that there exist at least two positive solutions of the problem for $λ∈Λ$.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n1.2}, url = {http://global-sci.org/intro/article_detail/jpde/5150.html} }
TY - JOUR T1 - Ground State Solutions for a Semilinear Elliptic Equation Involving Concave-convex Nonlinearities AU - Khazaee Kohpar , O. AU - Khademloo , Somayeh JO - Journal of Partial Differential Equations VL - 1 SP - 14 EP - 24 PY - 2013 DA - 2013/03 SN - 26 DO - http://doi.org/10.4208/jpde.v26.n1.2 UR - https://global-sci.org/intro/article_detail/jpde/5150.html KW - Semilinear elliptic equations KW - Nehari manifold KW - concave-convex nonlinearities AB -

This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem $-Δu=λa(x)u|u|^{q-2}+ b(x)u|u|^{2^∗-2}$ in a bounded domain coupled with Dirichlet boundary condition. Here $2^∗$ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions. Using the Nehari manifold method we prove that one can find an interval L such that there exist at least two positive solutions of the problem for $λ∈Λ$.

O. Khazaee Kohpar & Somayeh Khademloo. (2019). Ground State Solutions for a Semilinear Elliptic Equation Involving Concave-convex Nonlinearities. Journal of Partial Differential Equations. 26 (1). 14-24. doi:10.4208/jpde.v26.n1.2
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