Weak solutions for the singular potential wave system. (English) Zbl 1304.35409
Summary: We investigate the existence of weak solutions for a system of wave equations with singular potential nonlinearity. We obtain a theorem which shows the existence of nontrivial weak solutions for the wave system with Dirichlet boundary condition. We obtain this result by using the variational method and critical point theory for indefinite functionals.
MSC:
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 35B33 | Critical exponents in context of PDEs |
Keywords:
singular potential nonlinearity; Dirichlet boundary condition; variational method; \((PS)c\) conditionReferences:
| [1] | Benci V, Rabinowitz PH: Critical point theorems for indefinite functionals.Invent. Math. 1979, 52:241-273. 10.1007/BF01389883 · Zbl 0465.49006 · doi:10.1007/BF01389883 |
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