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Minimax principles for critical-point theory in applications to quasilinear boundary-value problems. (English) Zbl 0965.35060

Summary: Using the variational method developed [An abstract critical point theorem and applications to Hamiltonian systems (to appear)], we establish the existence of solutions to the equation \(-\Delta_p u = f(x,u)\) with Dirichlet boundary conditions. Here \(\Delta_p\) denotes the \(p\)-Laplacian and \(\int_0^s f(x,t) dt\) is assumed to lie between the first two eigenvalues of the \(p\)-Laplacian.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
49J35 Existence of solutions for minimax problems
35B34 Resonance in context of PDEs
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