Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $ℝ^N$

Daomin Cao; Ezzat S. Noussair

doi:10.1016/s0294-1449(16)30115-9

JournalsaihpcVol. 13, No. 5pp. 567–588

Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $R^{N}$

Daomin Cao
Wuhan Institute of Mathematical Sciences, The Chinese Academy of Sciences, P.O. Box 71007, Wuhan 430071, P.R. China
Ezzat S. Noussair
School of Mathematics, University of New South Wales, Sydney 2052 NSW, Australia

Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $ℝ^N$ cover

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Abstract

We are concerned with the multiplicity of positive and nodal solutions of

{- Δ u + μu = Q (x) ∣ u ∣^{p - 2} u u \in H^{1} (R^{N}) in R^{N}

where $2 < p < \frac{2 N}{N - 2}$ , $N \geq 3$ , $μ > 0$ , $Q \in C (R^{N})$ and $Q (x) \geq 0$ for $x \in R^{N}$ . We show how the “shape” of the graph of $Q (x)$ affects the number of both positive and nodal solutions.

Cite this article

Daomin Cao, Ezzat S. Noussair, Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $R^{N}$ . Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), no. 5, pp. 567–588

DOI 10.1016/S0294-1449(16)30115-9