Bifurcation for indefinite-weighted p $p$ -Laplacian problems with slightly subcritical nonlinearity

Pub Date : 2024-09-01 DOI:10.1002/mana.202400184
Mabel Cuesta, Rosa Pardo
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Abstract

We study a superlinear elliptic boundary value problem involving the p $p$ -Laplacian operator, with changing sign weights. The problem has positive solutions bifurcating from the trivial solution set at the two principal eigenvalues of the corresponding linear weighted boundary value problem.

Drabek's bifurcation result applies when the nonlinearity is of power growth. We extend Drabek's bifurcation result to slightly subcritical nonlinearities. Compactness in this setting is a delicate issue obtained via Orlicz spaces.

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具有轻微次临界非线性的不定加权 p$p$-Laplacian 问题的分岔问题
我们研究了一个涉及符号权重变化的-拉普拉茨算子的超线性椭圆边界值问题。Drabek 的分岔结果适用于幂级数增长的非线性问题。我们将 Drabek 的分岔结果扩展到略亚临界非线性问题。在这种情况下,紧凑性是一个通过奥立兹空间获得的微妙问题。
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