论文信息 - On semilinear elliptic equations with indefinite nonlinearities

On semilinear elliptic equations with indefinite nonlinearities

This paper concerns semilinear elliptic equations whose nonlinear term has the formW(x)f(u) whereW changes sign. We study the existence of positive solutions and their multiplicity. The important role played by the negative part ofW is contained in a condition which is shown to be necessary for homogeneousf. More general existence questions are also discussed.

Gabriella Tarantello | S. Alama | Stanley Alama | G. Tarantello

[1] V. Benci. On critical point theory for indefinite functionals in the presence of symmetries , 1982 .

[2] Haim Brezis,et al. Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents Haim Brezis , 2022 .

[3] P. Rabinowitz,et al. Dual variational methods in critical point theory and applications , 1973 .

[4] P. Rabinowitz. Minimax methods in critical point theory with applications to differential equations , 1986 .

[5] Michael G. Crandall,et al. Bifurcation, perturbation of simple eigenvalues, itand linearized stability , 1973 .

[6] Michael Struwe,et al. Variational methods: Applications to nonlinear partial differential equations and Hamiltonian systems , 1990 .

[7] Elliott H. Lieb,et al. A Relation Between Pointwise Convergence of Functions and Convergence of Functionals , 1983 .

[8] B. Simon,et al. On a theorem of Deift and Hempel , 1988 .

[9] R. Schoen,et al. Conformal metrics with prescribed scalar curvature , 1986 .

[10] C. Bandle,et al. Existence and uniqueness of solutions of nonlinear Neumann problems , 1988 .

[11] F. W. Warner,et al. Scalar curvature and conformal deformation of Riemannian structure , 1975 .