MULTIPLICITY OF SOLUTIONS AND SOURCE TERMS IN A NONLINEAR PARABOLIC EQUATION UNDER DIRICHLET BOUNDARY CONDITION

Abstract

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

Keywords

• nonlinear parabolic equation;
• Dirichlet boundary condition;
• multiplicity

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References

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