Existence of solutions for a system of diffusion equations with spectrum point zero. (English) Zbl 1293.35137
Summary: We consider the existence and multiplicity of homoclinic type solutions to a system of diffusion equations with spectrum point zero. By using some recent critical point theorems for strongly indefinite problems, we obtain at least one nontrivial solution and also infinitely many solutions.
MSC:
| 35K45 | Initial value problems for second-order parabolic systems |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 58E50 | Applications of variational problems in infinite-dimensional spaces to the sciences |
| 37C29 | Homoclinic and heteroclinic orbits for dynamical systems |
| 35K58 | Semilinear parabolic equations |
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