full
search.png

Search

close.png

Cancel

arrow
Volume 27, Issue 1
Multiple Positive Solutions for Semilinear Elliptic Equations Involving Subcritical Nonlinearities in RN

Somayeh Khademloo & Rahelh Mohsenhi

DOI: 10.4208/jpde.v27.n1.5

J. Part. Diff. Eq., 27 (2014), pp. 74-94.

Published online: 2014-03

Preview Full PDF 2674 34183

Cited by

google scholar semantic scholar
Export citation
  • Abstract
In this paper, we study how the shape of the graph of a(z) affects on the number of positive solutions of $$-\Delta\upsilon+μ b(z)\upsilon^{p-1}+λ h(z)\upsilon^{q-1}, \qquad\;in\; \mathbb{R}^N.\qquad (0.1)$$ We prove for large enough λ,μ › 0, there exist at least k+1 positive solutions of the this semilinear elliptic equations where 1 ≤ q ‹ 2 ‹ p ‹ 2*|=2N/(N-2) for N ≥ 3.
  • Keywords

Sobolev spaces semilinear elliptic equations critical exponent Nehari manifold Palais-Smale condition

  • AMS Subject Headings

35J20, 35J25, 35J65

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

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

rm_omran78@yahoo.com (Rahelh Mohsenhi)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-27-74, author = {Khademloo , Somayeh and Mohsenhi , Rahelh}, title = {Multiple Positive Solutions for Semilinear Elliptic Equations Involving Subcritical Nonlinearities in RN}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {1}, pages = {74--94}, abstract = { In this paper, we study how the shape of the graph of a(z) affects on the number of positive solutions of $$-\Delta\upsilon+μ b(z)\upsilon^{p-1}+λ h(z)\upsilon^{q-1}, \qquad\;in\; \mathbb{R}^N.\qquad (0.1)$$ We prove for large enough λ,μ › 0, there exist at least k+1 positive solutions of the this semilinear elliptic equations where 1 ≤ q ‹ 2 ‹ p ‹ 2*|=2N/(N-2) for N ≥ 3.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/5127.html} }
TY - JOUR T1 - Multiple Positive Solutions for Semilinear Elliptic Equations Involving Subcritical Nonlinearities in RN AU - Khademloo , Somayeh AU - Mohsenhi , Rahelh JO - Journal of Partial Differential Equations VL - 1 SP - 74 EP - 94 PY - 2014 DA - 2014/03 SN - 27 DO - http://doi.org/10.4208/jpde.v27.n1.5 UR - https://global-sci.org/intro/article_detail/jpde/5127.html KW - Sobolev spaces KW - semilinear elliptic equations KW - critical exponent KW - Nehari manifold KW - Palais-Smale condition AB - In this paper, we study how the shape of the graph of a(z) affects on the number of positive solutions of $$-\Delta\upsilon+μ b(z)\upsilon^{p-1}+λ h(z)\upsilon^{q-1}, \qquad\;in\; \mathbb{R}^N.\qquad (0.1)$$ We prove for large enough λ,μ › 0, there exist at least k+1 positive solutions of the this semilinear elliptic equations where 1 ≤ q ‹ 2 ‹ p ‹ 2*|=2N/(N-2) for N ≥ 3.
Khademloo , Somayeh and Mohsenhi , Rahelh. (2014). Multiple Positive Solutions for Semilinear Elliptic Equations Involving Subcritical Nonlinearities in RN. Journal of Partial Differential Equations. 27 (1). 74-94. doi:10.4208/jpde.v27.n1.5
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard