一类半线性双曲型微分不等式非齐次 Dirichlet 外问题解的存在性与非存在性

Abstract

Abstract:

This paper is concerned with the nonhomogeneous Dirichlet exterior problem for a semilinear hyperbolic differential inequality in the higher dimensional space ($N\geq2$). Using the test function method and contradiction argument, we establish the nonexistence theorem under the nonhomogeneous Dirichlet boundary condition, which depends both on time and space. Meantime, we obtain some existence results.

Key words: Hyperbolic differential inequality, Nonhomogeneous Dirichlet exterior problem, Existence, Nonexistence

CLC Number:

O175.23

Xiao Suping, Zhao Yuanzhang. Existence and Nonexistence of Solutions for Nonhomogeneous Dirichlet Exterior Problem to a Semilinear Hyperbolic Differential Inequality[J].Acta mathematica scientia,Series A, 2024, 44(5): 1167-1182.

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Existence and Nonexistence of Solutions for Nonhomogeneous Dirichlet Exterior Problem to a Semilinear Hyperbolic Differential Inequality

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