含奇异梯度项的p-k-Hessian系统爆破解的存在性和非存在性

Existence and Nonexistence of Blow-Up Solutions for p-k-Hessian System with Singular Gradient Terms

摘要

利用单调迭代方法,研究一类含有奇异梯度项的p-k-Hessian系统p-k-凸径向解的存在性和有界性,并给出有界解的范围估计.在关于非线性项的适当假设条件下,得到爆破解的存在性和非存在性,并给出几个实例验证所得结论.

Abstract

By using the monotonic iterative method, we studied the existence and boundedness of p-k-convex radial solutions for a class of p-k-Hessian systems with singular gradient terms, and gave the range estimate of bounded solutions. Under appropriate assumptions about nonlinear terms, we obtained the existence and nonexistence of blow-up solutions, and gave several examples to verify the obtained conclusions.

关键词

p-k-Hessian系统 / 奇异梯度项 / 爆破解 / 非存在性

Key words

p-k-Hessian system / singular gradient term / blow-up solution / nonexistence

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基金资助

国家自然科学基金(12371173)

山东省自然科学基金(ZR2021MA064)