Concepedia

Existence of solutions to Δ<sub>λ</sub>-Laplace equations without the Ambrosetti–Rabinowitz condition

Cung The Anh, Bui Kim My

Complex Variables and Elliptic Equations · 2015 · 34 citations · 13 references

DOI

Concepts

Abstract

We study the existence of nontrivial weak solutions for the following boundary value problemwhere is a bounded domain in , is a strongly degenerate elliptic operator, the nonlinearity is subcritical growth and does not satisfy the Ambrosetti–Rabinowitz (AR) condition.

References

13

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, , +14

Superlinear problems without Ambrosetti and Rabinowitz growth condition

Olı́mpio H. Miyagaki, Marco A. S. Souto · Journal of Differential Equations · 2008 · 204 citations · Full text

, , +1

On the Ambrosetti-Rabinowitz Superlinear Condition

Zhaoli Liu, Zhiqiang Wang · Advanced Nonlinear Studies · 2004 · 166 citations

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On semilinear -Laplace equation

Alessia E. Kogoj, Ermanno Lanconelli · Nonlinear Analysis · 2011 · 131 citations

, , +9

Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition

Nguyen Lam, Guozhen Lu · Journal of Geometric Analysis · 2012 · 114 citations

, , +14