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NONHOMOGENEOUS, NONAUTONOMOUS RESONANT SINGULAR EQUATIONS
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DOI：10.23952/jnva.10.2026.1.05.png)
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Abstract
En 中文
We consider a nonlinear Dirichlet problem driven by a nonautonomous (p, q)-differential operator and with a reaction having the competing effects of a parametric singular term and a (p - 1)linear perturbation which can be resonant as x -> infinity with respect to the principal eigenvalue of the relevant operator. If the resonance is from the left, then we demonstrate that the problem has a positive solution for all values of the parameter and if the driving differential operator is only the nonautonomous pLaplacian, then the positive solution is unique. On the other hand, if the resonance is from the right, then we prove an existence and multiplicity theorem which is global with respect to the parameter (a bifurcation-type theorem). Also, we conduct a detailed study of the continuity properties of solution multifunction.
Keywords:
Nonautonomous (p, q)-operator
Resonance
Hardy's inequality
Singular and superlinear terms
Multiple solutions
Continuity of the solution multifunction
Journal
IF:
1.9
Papers:
72
Citations:
356
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